## 统计代写|工程统计作业代写Engineering Statistics代考|Values of Distributions and Inverses

statistics-lab™ 为您的留学生涯保驾护航 在代写工程统计Engineering Statistics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写工程统计Engineering Statistics代写方面经验极为丰富，各种代写工程统计Engineering Statistics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|工程统计作业代写Engineering Statistics代考|For Continuum-Valued Variables

For continuum-valued variables, $x$, the cumulative distribution function is the probability of getting a particular value or a lower value of a variable. It is the left-sided area on the probability density curve, often expressed as alpha. It is variously represented as $C D F(x)=F(x)=\alpha=p$. Here we ll use the $C D F(x)$ notation.

For continuous-valued variables, $x$, the probability distribution function, $p d f(x)$, represents the rate of increase of probability of occurrence of the value $x$. An alternate notation is $p d f(x)=f(x)$.

The relation between CDF(x) and $p d f(x)$ is
$$\operatorname{CDF}(x)=\int_{x_{\text {mimeme }}}^{x} p d f(x) d x$$
Where $x_{\text {minimun }}$ represents the lowest possible value for $x$. In a normal distribution $x_{\operatorname{minimum}}=$ $-\infty$. For a chi-squared distribution $x_{\text {minimun }}=0$.

The left-hand sketch in Figure $3.16$ illustrates the $C D F$ and the right-hand sketch the $p d f$ of $z$ for a standard normal distribution (the mean is zero and the standard deviation is unity). At a value of $z=-1$, the $C D F$ is about $0.158$, and the rate of increase of the $C D F$, the $p d f$ is about $0.242$. The notations are $0.158=C D F(-1)$ and $0.242=p d f(-1)$. In both you enter the graph on the horizontal axis, the $z$-value, and read the value on the vertical axis.

For continuous-valued variables the inverse of the CDF is the value of $x$ for which the probability of getting the value of $x$ or a lower value is equal to the CDF $(x)$.

The inverse would enter on the vertical axis to read the value on the horizontal axis. If the inverse question is, “What $z$-value marks the point for which equal or lower $z$-values have a probability of $0.158$ of occurring?” then we represent this inverse question as $z=\operatorname{CDF}^{-1}(\alpha)$. In this illustration, $-1=\operatorname{CDF}^{-1}(0.158)$. The inverse of the right-hand $p d f$ graph is not unique. If the question is to determine the $z$-value for which the $p d f=0.242$, there are two values, $z=-1$, and $z=+1$.

## 统计代写|工程统计作业代写Engineering Statistics代考|For Discrete-Valued Variables

For discrete-valued variables, $x$, likely a count of the number of events, the cumulative distribution function is the probability of getting a particular value or a lower value of a variable. It is the left-sided area on the probability density curve, often expressed as alpha. It is variously represented as $\operatorname{CDF}(x)=F(x)=\alpha=p$. Again, we will use the $C D F(x)$ notation.
For discrete-valued variables, $x$, the point distribution function, $p d f(x)$, represents the probability of an occurrence of the value $x$. An alternate notation is $p d f(x)=f(x)$. Here, $p d f(x)$ is a probability of a particular value of $x$, not the rate that the CDF is increasing. Unfortunately, the same symbol is used in continuum-valued distribution.
The relation between $\operatorname{CDF}(x)$ and $p d f(x)$ is
$$\operatorname{CDF}(x)=\sum_{x_{\text {meimum }}}^{x} p d f(x)$$

where $x_{\text {minimum }}$ represents the lowest possible value for $x$. Normally $x_{\text {minimum }}=0$, the least number of events that could occur.

The left-hand sketch of Figure $3.17$ illustrates the CDF and the right-hand sketch the $p d f$ of $s$, the count of the number of successes, for a binomial distribution (the number of trials is 40 , and the probability of success on any particular trial is $0.3$ ). Note that the markers on the graphs represent feasible values. The light line connecting the dots is a visual convenience. It is not possible to have $10.3$ successes. At a value of $s=10$, the CDF is about $0.309$, meaning that there is about a $31 \%$ chance of getting 10 or fewer successes. The $p d f$ is about $0.113$, meaning that the probability of getting exactly 10 successes is about $11 \%$. The notations are $0.309=\operatorname{CDF}(10)$ and $0.113=p d f(10)$. In both you enter the graph on the horizontal axis, the $s$-value, and read the value on the vertical axis.

For discrete-valued variables the inverse of the $C D F$ is the value of $s$ for which the probability of getting the value of $s$ or a lower value is equal to the CDF(s).
The inverse would enter on the vertical axis to read the value on the horizontal axis. If the inverse question is, “What $s$-value marks the point for which equal or lower counts have a probability of $0.309$ of occurring?” then we represent this inverse question as $s=C D F^{-1}(\alpha)$. In this illustration, $10=C D F^{-1}(0.309)$. The inverse of the right-hand pdf graph appears to be not unique. However, it might be. If the question is to determine the s-value for which the $p d f=0.113$, there is only one value, $s=10$. It appears that an $s$-value of about $13.5$ could have such a CDF value, but the count must be an integer. The $p d f$ of $S=13$ is $0.126$, and the $p d f$ of $S=14$ is $0.104$.

Although one could ask, “What count value, or lower, has a $30 \%$ chance of occurring?” it is impossible to match the $30 \% C D F=0.3 \overline{000}$ value. $S \leq 9$ has a $C D F$ of about $0.196$ which does not include the target $0.3 \overline{000} . S \leq 10$ has a CDF of about $0.309$ which does match. $S=10$ is the lowest value that includes the target $C D F$. One convention is to report the minimum count that includes the target $C D F$ value.

## 统计代写|工程统计作业代写Engineering Statistics代考|Propagating Distributions with Variable Transformations

Often, we know the distribution on $x$-values and have a model that transforms $x$ to $y$. For instance, $y=\operatorname{Ln}(x)$. The question is, “What is the distribution of $y$ ?”

Figure $3.18$ reveals the case of $y=a+b x^{3}$ when the distribution on $x$ (on the abscissa) is normal.

Note: For the range of $x$-values shown, the function is strictly monotonic, positive definite. As $x$ increases, $y$ increases for all values of $x$. There are no places in the $x$-range where either 1) the derivative is negative or 2) zero (there are no flat spots in the function).

The inset sketches indicate the $p d f$ (dashed line) and CDF of $x$ and $y$, about a nominal value of $x_{0}=2.5$ and the corresponding $y_{0}=a+b x_{0}{ }^{3}$. Note that the $p d f$ of $x$ is symmetric, and that of $y$ is skewed.

The CDF of $x$ indicates the probability that $x$ could have a lower value. For any $x$ there is a corresponding $y$, and since the function is strictly monotonic, the probability of a lower $y$-value is the same as the probability of a lower $y$-value. Then
$$\operatorname{CDF}(y=f(x))=\operatorname{CDF}(x)$$
Between any two corresponding points $x_{1}$ and $x_{2}$ separated by $\Delta x=x_{2}-x_{1}$, there are the two corresponding points $y_{1}=f\left(x_{1}\right)$ and $y_{2}=f\left(x_{2}\right)$ separated by $\Delta y=f\left(x_{2}\right)-f\left(x_{1}\right) \cong \frac{d y}{d x} \Delta x$ for small $\Delta x$ values (meaning that $\frac{d y}{d x}$ is relatively unchanged over the $\Delta x$ interval). Since $\operatorname{CDF}\left(y_{2}\right)=\operatorname{CDF}\left(x_{2}\right)$ and $\operatorname{CDF}\left(y_{1}\right)=\operatorname{CDF}\left(x_{1}\right)$, the difference is also equal, and by definition:
$$\int_{y_{1}}^{y_{2}} p d f(y) d y=\int_{x_{1}}^{x_{2}} p d f(x) d x$$
For small $\Delta x$ intervals, the integral can be approximated by the trapezoid rule of integration, and in the limit of very small $\Delta x$,

To obtain the $C D F(y)$ numerically integrate the $p d f(y)$. Using the trapezoid rule of integration, with y sorted in ascending order.
$$\operatorname{CDF}\left(y_{i+1}\right)=\operatorname{CDF}\left(y_{i}\right)+\frac{1}{2}\left[p d f\left(y_{i+1}\right)+p d f\left(y_{i}\right)\right]\left(y_{i+1}-y_{i}\right)$$
Initialize $C D F\left(y_{\text {very low }}\right)=0$.

## 统计代写|工程统计作业代写Engineering Statistics代考|For Continuum-Valued Variables

CDF(x) 与pdF(X)是
CDF⁡(X)=∫X哑剧 XpdF(X)dX

## 统计代写|工程统计作业代写Engineering Statistics代考|For Discrete-Valued Variables

CDF⁡(X)=∑X最大 XpdF(X)

## 统计代写|工程统计作业代写Engineering Statistics代考|Propagating Distributions with Variable Transformations

CDF 的X表示概率X可能有较低的价值。对于任何X有对应的是，并且由于该函数是严格单调的，因此较低的概率是-值与较低的概率相同是-价值。然后
CDF⁡(是=F(X))=CDF⁡(X)

∫是1是2pdF(是)d是=∫X1X2pdF(X)dX

CDF⁡(是一世+1)=CDF⁡(是一世)+12[pdF(是一世+1)+pdF(是一世)](是一世+1−是一世)

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|工程统计作业代写Engineering Statistics代考|“Student’s” t-Distribution

statistics-lab™ 为您的留学生涯保驾护航 在代写工程统计Engineering Statistics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写工程统计Engineering Statistics代写方面经验极为丰富，各种代写工程统计Engineering Statistics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|工程统计作业代写Engineering Statistics代考|“Student’s” t-Distribution

W. S. Gossett, publishing his work under the pseudonym “Student,” developed the $t$-distribution. The statistic would become the basis for the $t$-test so widely used for the evaluation of engineering data.

The $t$-statistic is very similar to the standard normal $z$-statistic, but instead of using the true population mean and standard deviation, it uses the sample standard deviation.
$$T=\frac{X-\mu}{s}$$
Because it is based on sample data, not the entire population, the degrees of freedom $\nu$ is one less than the number of data used to calculate the sample average and $s$
$$v=n-1$$
Relative to the $z$-statistic, the $t$-statistic includes the uncertainty on both the sample average and sample standard deviation. Both the $z$ – and t-statistics are dimensionless regardless of the units on the variable $X$.
The random variable $t$ has the probability density function below:
$$\begin{gathered} f(t)=\frac{1}{\sqrt{v \pi}} \frac{\Gamma((v+1) / 2)}{\Gamma(v / 2)}\left(1+\frac{t^{2}}{v}\right)^{-(v+1) / 2} \text { for }-\infty<t<\infty \ C D F(t)=F(t)=\frac{1}{\sqrt{v \pi}} \frac{\Gamma((v+1) / 2)}{\Gamma\left(\frac{v}{2}\right)} \int_{-\infty}^{t}\left(1+\frac{x^{2}}{v}\right)^{-(v+1) / 2} d x \end{gathered}$$

Note that $\Gamma(v / 2)$ is the gamma function. The gamma function is related to the factorial and is not the gamma probability density distribution. Like the $z$-distribution, the distribution of $t$ is bilaterally symmetric about $t=0$. The $t$-distribution is illustrated in Figure $3.11$ for two values of $v$, the degrees of freedom. The resulting bell-shaped distribution resembles that of the standard normal. However, more of the area under the $t$-distribution is in the “tails” of the distribution. In the limit of large $n$ (effectively $\nu$ greater than about 150) the $t$ – and standard normal distributions differ in the tenths of a percent.

The use of the $t$-distribution will be described in subsequent chapters in the sections discussing confidence intervals and tests of hypotheses for the mean of experimental distributions.

The cumulative $t$-distribution, $F(t)$ from Equation (3.60) can be calculated by the Excel function T.DIST $(t, v, 1)$ where $t$ is calculated from the sample data. Alternately, if you wanted to know the $t$-value that represents a probability limit then use the Excel function T.INV $(C D F, v)$ to return a $t$-value that would represent that $C D F$ value. Alternately, calculate $\alpha$, the level of significance, the extreme right-hand area, as $\alpha=1-F(t)=1-C D F$, then use the Excel function T.INV $(1-\alpha, v)$.

That represented a one-sided evaluation, which considered the area under the $t$-distribution from $-\infty$ up to a particular $t$-value. But often, we desire to know either the positive or negative extreme values for $t$, the ” $t$ ” or “- ” deviations from the central “0” value. You may want to know the range of $t$-values that includes the central $95 \%$ (or some confidence fraction C) of all expected values from sampling the population.
$$P\left(t_{\text {negative limit }} \leq T \leq t_{\text {positive limit }}\right)=C$$
Here, the level of significance is again the extreme area. If the $95 \%$ interval is desired $(C=$ $0.95$ ) then $\alpha=1-0.95=1-C$. Splitting the two tail areas equally, to define the central limits, use $\alpha / 2$ to represent both the far right and far left areas in the tails. Then we seek the $t$-value calculated with $F(t)=1-\alpha / 2$. The Excel function T.INV $(1-\alpha / 2, v)$ will return the $t$-value representing the positive extreme expected value, and $-T$.INV $(1-\alpha / 2, v)$ will return the negative extreme. This is termed a two-sided (historically a two-tailed) test, because we are seeking the limits of the central area. Alternately, $T$.INV.2T $(1-\alpha, v)$ returns the same value.

## 统计代写|工程统计作业代写Engineering Statistics代考|Chi-Squared Distribution

Let $Y_{\nu} Y_{2}, Y_{3}, \ldots, Y_{n}$ be independent random variables each distributed with mean 0 and variance 1 . The random variable chi-squared:
$$\chi^{2}=\sum_{i=1}^{n} Y_{i}^{2}$$
has the chi-squared probability density function with $v=n-1$ degrees of freedom
$$f\left(\chi^{2}\right)=\frac{1}{2^{v / 2} \Gamma(v / 2)}\left[e^{-\chi^{2} / 2}\right]\left[\chi^{2}\right]^{(v / 2)-1} \text { for } 0 \leq \chi^{2} \leq \infty$$
and cumulative distribution
$$F\left(\chi^{2}\right)=\frac{1}{2^{v / 2} \Gamma(v / 2)} \int_{0}^{\chi^{2}} e^{-Y / 2}(Y)^{(v / 2)-1} d Y$$
If $Y$ in Equation (3.62) is defined as $(X-\bar{X}) / \sigma$ then
$$\chi^{2}=\sum_{i=1}^{n} Y_{i}^{2}=\sum_{i=1}^{n} \frac{\left(X_{i}-\bar{X}\right)^{2}}{\sigma^{2}}=\frac{(n-1) s^{2}}{\sigma^{2}}$$
Figure $3.12$ illustrates the probability density and cumulative chi-squared distributions, respectively. Values of the cumulative chi-squared $\left(\chi^{2}\right)$ distribution can be obtained from the Excel function $F\left(\chi^{2}\right)=\operatorname{CHISQ.DIST}\left(\chi^{2}, v, 1\right)$, and the $p d f$ by using $f\left(\chi^{2}\right)=$ CHISQ.DIST $\left(\chi^{2}, v, 0\right) .$

The inverse of the calculation, the value of $\chi^{2}$ given $F\left(x^{2}\right)$ and $v$ can be obtained by the Excel function $\chi^{2}=\mathrm{CHISQ} \cdot \mathrm{INV}(F, v)$.

Note: Some tables or procedures use $\chi^{2} / v$. Since Equation (3.62) indicates that $\chi^{2}$ increases linearly with $n$, and since degrees of freedom is often $v=n-1$, the scaling makes

sense. Mostly, this book will not scale $\chi^{2}$ by the degrees of freedom. But be aware that the use of either $\chi^{2} / v$ or $\chi^{2}$ is common.
The mean and variance of the chi-squared distribution are $v$ and $2 v$, respectively.
$$\begin{gathered} \mu=v \ \sigma=2 v \end{gathered}$$
So, if degrees of freedom is 10 , an average-like value of the $\chi^{2}$ statistic would be about 10 . $x^{2}=1$ would be an unexpectedly low value, and $\chi^{2}=20$ would be unexpectedly high.
This distribution has several applications, one of which is in calculating and evaluating probability intervals for single variances from normally distributed populations as shown in Chapters 5 and 6. The chi-squared distribution is also used as a nonparametric method of determining whether or not, based on sample data, a population has a particular distribution, as described in Chapter 7 . The chi-squared distribution goes from 0 to infinity, or $P\left(0 \leq \chi^{2} \leq \infty\right)=1 .$
The interval
$$P\left(\chi_{v, \alpha / 2}^{2} \leq \chi^{2} \leq \chi_{v, 1-\alpha / 2}^{2}\right)=1-\alpha$$
defines the values for the $\chi^{2}$-distribution such that equal areas are in each tail. The $x^{2}$-distribution is not symmetric about the mean as are the $Z$ – and $t$-distributions.

## 统计代写|工程统计作业代写Engineering Statistics代考|F-Distribution

The F-distribution (named in honor of Sir Ronald Fisher, who developed it) is the distribution of the random variable $F$, defined as
$$F=\frac{U / v_{1}}{V / v_{2}}=\frac{\chi_{1}^{2} / v_{1}}{\chi_{2}^{2} / v_{2}}$$
Using Equation (3.65) $\chi^{2}=\frac{(n-1) s^{2}}{\sigma^{2}}=\frac{v s^{2}}{\sigma^{2}}$
$$F=\frac{s_{1}^{2} / \sigma_{1}^{2}}{s_{2}^{2} / \sigma_{2}^{2}}$$
where $U$ and $V$ are independent variables distributed following the chi-squared distribution with $v_{1}$ and $v_{2}$ degrees of freedom, respectively. The symbol $F$ in Equation (3.69) does not represent any cumulative distribution but is a statistic, specifically, the ratio of two $\chi^{2}$ statistics, each scaled by their degrees of freedom. The probability density function of $F$ is
$$f(F)=\frac{\Gamma\left(\left(v_{1}+v_{2}\right) / 2\right)}{\Gamma\left(v_{1} / 2\right) \Gamma\left(v_{2} / 2\right)}\left(\frac{v_{1}}{v_{2}}\right)^{v_{1} / 2} \frac{F^{\left(v_{1}-2\right) / 2}}{\left(1+\left(v_{1} / v_{2}\right) F\right)^{\left(v_{1}+v_{2}\right) / 2}}$$
and the cumulative distribution of $F$ is
$$C D F(F)=\int_{0}^{F} f(F) d F$$

The family of F-distributions is a two-parameter family in $v_{1}$ and $v_{2}$. The shape of the F-distribution is skewed (more of the area under the curve to the left side of the nominal value, a longer tail to the right), as illustrated in Figure 3.13. The range of all members is from 0 to $\infty$. This distribution is used to evaluate equality of variances. The $F$-distribution is termed “robust” by statisticians, meaning that the results of such statistical comparisons are likely to be valid even if the underlying populations are not normally distributed. The uses of the F-distribution are explained in Chapters 5, 6, and $12 .$

Values of the $p d f(F)$ can be returned by the Excel function $p d f(F)=F$.DIST $\left(\chi_{1}^{2} / \chi_{2}^{2}, v_{1}, v_{2}, 0\right)$, and of the cumulative $F$-distribution by $\operatorname{CDF}(F)=F$.DIST $\left(\chi_{1}^{2} / \chi_{2}^{2}, v_{1}, v_{2}, 1\right)$. The inverse of the distribution returns the chi-squared ratio for a given $C D F$ value $\frac{\chi_{1}^{2}}{\chi_{2}^{2}}=F$ INV $\left(C D F, v_{1}, v_{2}\right)$.
If the chi-squared ratio is $3.58058$ and the numerator and denominator degrees of freedom are 6 and 8 , then the CDF value is $0.95$. If, however, you choose to call #1 as #2, then the chi-squared ratio would be $0.279284$, and the degrees of freedom would be 8 then 6 . With these reversed values the $C D F$ value is $0.05$ the complement to the first.

## 统计代写|工程统计作业代写Engineering Statistics代考|“Student’s” t-Distribution

WS Gossett 以笔名“学生”出版了他的作品，开发了吨-分配。该统计数据将成为吨-test 如此广泛地用于评估工程数据。

F(吨)=1在圆周率Γ((在+1)/2)Γ(在/2)(1+吨2在)−(在+1)/2 为了 −∞<吨<∞ CDF(吨)=F(吨)=1在圆周率Γ((在+1)/2)Γ(在2)∫−∞吨(1+X2在)−(在+1)/2dX

## 统计代写|工程统计作业代写Engineering Statistics代考|Chi-Squared Distribution

χ2=∑一世=1n是一世2

F(χ2)=12在/2Γ(在/2)[和−χ2/2][χ2](在/2)−1 为了 0≤χ2≤∞

F(χ2)=12在/2Γ(在/2)∫0χ2和−是/2(是)(在/2)−1d是

χ2=∑一世=1n是一世2=∑一世=1n(X一世−X¯)2σ2=(n−1)s2σ2

μ=在 σ=2在

## 统计代写|工程统计作业代写Engineering Statistics代考|F-Distribution

F 分布（以开发它的 Ronald Fisher 爵士的名字命名）是随机变量的分布F， 定义为
F=在/在1在/在2=χ12/在1χ22/在2

F=s12/σ12s22/σ22

F(F)=Γ((在1+在2)/2)Γ(在1/2)Γ(在2/2)(在1在2)在1/2F(在1−2)/2(1+(在1/在2)F)(在1+在2)/2

CDF(F)=∫0FF(F)dF

F 分布族是一个二参数族在1和在2. 如图 3.13 所示，F 分布的形状是倾斜的（曲线下面积在标称值左侧的更多，在右侧的尾部较长）。所有成员的范围是从0到∞. 此分布用于评估方差的相等性。这F-分布被统计学家称为“稳健”，这意味着即使基础人口不是正态分布的，这种统计比较的结果也可能是有效的。第 5、6 章和第 5 章解释了 F 分布的使用。12.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|工程统计作业代写Engineering Statistics代考|Exponential Distribution

statistics-lab™ 为您的留学生涯保驾护航 在代写工程统计Engineering Statistics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写工程统计Engineering Statistics代写方面经验极为丰富，各种代写工程统计Engineering Statistics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|工程统计作业代写Engineering Statistics代考|Continuous Distributions

The exponential (or negative exponential) distribution describes a mechanism whereby the probability of failures (or events) within a time or distance interval depends directly on the number of un-failed items remaining. It describes events such as radioisotope decay, light intensity attenuation through matter of uniform properties, the failure rate of light bulbs, and the residence time or age distribution of particles in a continuous-flow stirred tank. Requirements for the distribution are that, at any time, the probability of any one particular item failing is the same as that of any other item failing and is the same as it was earlier. Another restriction is that the numbers are so large that the measured values seem to be a continuum. The probability distribution functions are
$$p d f(x)=\alpha e^{-\alpha x}, \quad 0 \leq x \leq \infty, \quad \alpha>0$$
and
$$F(x)=1-e^{-\alpha x}$$
The variable $x$ represents the time or distance interval, not the number (or some other measure of quantity) of un-failed items. The argument of an exponential must be dimensionless,

so the units on $\alpha$ are the reciprocal of the units on $x$. This requires that the units on $p d f(x)$ are also the reciprocal of the units on $x$, making $p d f(x)$ be a rate.

Figure $3.8$ illustrates the exponential distribution for $\alpha=0.3$. The mean and variance of the exponential distribution are
$$\mu=\frac{1}{\alpha}$$
and
$$\sigma^{2}=\frac{1}{\alpha^{2}}$$
The continuous random variable $X$ may have any units. The units on $\mu$ will be the same. The units on both $\alpha$ and $f(x)$ are the reciprocal of those of $X . F(x)$ is dimensionless. For a physical interpretation, $\alpha$ represents the fraction of events occurring per unit of space or time. The discrete geometric distribution, in its limit as the number of events is very large and the probability of success is small, approaches the continuous exponential distribution.
Example 3.10: One billion adsorption sites are available on the surface of a solid particle. Gas molecules, randomly and uniformly “looking” for a site, find one upon which to adsorb, which “hides” that site from other molecules. With an infinite gas volume, the rate at which the sites are occupied is therefore proportional to the number of unoccupied sites. If $40 \%$ of the sites are covered within the first 24 hours, how long will it take for $99 \%$ of the adsorption to be complete? What is the average lifetime of an unoccupied site?
From Equation (3.43),
$$40 \%=0.40=F(t)=1-e^{-a t}=1-e^{-a(24)}$$
which gives $\alpha=0.02128440 \ldots$ per hour. From Equation (3.43), $99 \%=0.99=F(t)=1-$ $e^{0.02128 .1}$, which gives $t=216.3636244$… hours or about 9 days. From Equation (3.44), $\mu=$ $1 / \alpha=46.9827645$ hours or almost 2 days.

## 统计代写|工程统计作业代写Engineering Statistics代考|Gamma Distribution

The gamma distribution can represent two mechanisms. In a general situation in which a number of partial random events must occur before a complete event is realized, the probability density function of the complete event is given by the gamma distribution. For instance, rust spots on your car (the partial event), may occur randomly at an average rate of one per month. If 16 spots occur before you decide to have your car repainted (the total event), the gamma distribution is the appropriate one to use to describe the repainting time interval. The gamma distribution is
$$p d f(x)=\frac{\lambda}{\Gamma(\alpha)}(\lambda x)^{\alpha-1} \exp (-\lambda x), x \geq 0$$
and where $\alpha$ and $\lambda>0$ and $\Gamma(\alpha)$ is the gamma function
$$\Gamma(\alpha)=\int_{0}^{\infty} Z^{\alpha-1} e^{-z} d Z$$
The gamma function has several properties
$$\Gamma(\alpha)=(\alpha-1) \Gamma(\alpha-1)$$
and if $\alpha$ is an integer, then
$$\Gamma(\alpha)=(\alpha-1) !$$
The variable $\alpha$ represents the number of partial events required to constitute a complete event, and $\lambda$ is the number of partial events per unit of $x$ (which may be time, distance, space, or item).

If $\alpha=1$, the gamma distribution reduces to the exponential distribution. For that reason, if an event rate is proportional to some power of $x$, then the gamma distribution can also be used as an adjusted exponential distribution. Let’s look at Example $3.10$ again. If adsorption reduces the number of gas molecules available for subsequent adsorption, then the probability of any site being occupied decreases with time. If the frequency with which gas molecules impinge on the particle surface decreases as $(\lambda x)^{a-1}$, then the gamma function describes $f(x)$. However, although close enough for most engineering applications, the power law decrease probably does not describe a real driving force exactly. For such a situation, use of the gamma distribution must be acknowledged as a convenient approximation.
Depending on the values of $\alpha$ and $\lambda, f(x)$ may have various shapes, some of which are illustrated in Figure 3.9. A general analytical expression for $F(x)$ is intractable. For most $\alpha$ values, to obtain the cumulative distribution function, $f(x)$ must be integrated numerically. Excel provides the function GAMMA.DIST $(x, \alpha, 1 / \lambda, 0)$ to return the $p d f(x)$ value

and GAMMA.DIST $(x, \alpha, 1 / \lambda, 1)$ to return the CDF $(x)$ value. Note that the Excel parameter beta is the reciprocal of $\lambda$, here.
The mean and variance of the gamma distribution are
\begin{aligned} \mu &=\frac{\alpha}{\lambda} \ \sigma^{2} &=\frac{\alpha}{\lambda^{2}} \end{aligned}
The units of $X$ are usually count per some interval (time, distance, area, space, or item). Consequently, the units for $\lambda$ are the fraction of total failures per unit of $X$. The coefficient, $\boldsymbol{\alpha}$, is a counting number and is dimensionless, and $f(x)$ has units that are the reciprocal of the units of $X$.

## 统计代写|工程统计作业代写Engineering Statistics代考|Normal Distribution

The normal distribution, often called the Gaussian distribution or bell-shaped error curve, is the most widely used of all continuous probability density functions. The assumption behind this distribution is that any errors (sources of deviation from true) in the experimental results are due to the addition of many independent small perturbation sources. All experimental situations are subject to many random errors and usually yield data that can be adequately described by the normal distribution.

Even if your data is not normally distributed, the averages of data from a nonnormal distribution tend toward being normal. An average of independent samples will have some values above the mean and some below. The average will be close to the mean, and each sample would represent a small independent deviation. In the limit of large sample size, $n$, the standard deviation of the average is related to that of the individual data by $\sigma_{\bar{X}}=\sigma_{X} / \sqrt{n}$. So, when using averages, the normal distribution usually is applicable.
However, this situation is not always true. If you have any doubt that your data are distributed normally, you should use the nonparametric techniques in Chapter 7 to evaluate the distribution. Use of statistics that depend on the normal distribution for a dataset that is distinctly skewed may lead to erroneous results.

An acronym for data that is normally and independently distributed with a mean of $\mu$ and standard deviation of $\sigma$ is $\operatorname{NID}(\mu, \sigma)$.

Regardless of the shape of the distribution of the original population, the central limit theorem allows us to use the normal distribution for descriptive purposes, subject to a single restriction. The theorem simply states that if the population has a mean $\mu$ and a finite variance $\sigma^{2}$, then the distribution of the sample mean $\bar{X}$ approaches the normal distribution with mean $\mu$ and variance $\sigma^{2} / n$ as the sample size $n$ increases. The chief problem with the theorem is how to tell when the sample size is large enough to give reasonable compliance with the theorem. The selection of sample sizes is covered in Chapters 10,11 , and $17 .$
The probability density function $f(x)$ for the normal distribution is
$$f(x)=\frac{1}{\sigma \sqrt{2 \pi}} \mathrm{e}^{\left[-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^{2}\right]},-\infty<x<\infty$$

Note that the argument of the exponentiation, $\left[-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^{2}\right]$, must be dimensionless. As expected, $x, \mu$, and $\sigma$ each have identical units. The exponentiation value is also dimensionless. Also, since $f(x)$ is proportional to $1 / \sigma$, it has the reciprocal units of $x$.

As seen in Equation (3.52), the normal distribution has two parameters, $\mu$ and $\sigma$, which are the mean and standard deviation, respectively. The cumulative distribution function $(C D F)$, described by
$$\operatorname{CDF}(x)=F(x)=P(X \leq x)=\frac{1}{\sigma \sqrt{2 \pi}} \int_{-\infty}^{x} e^{-(X-\mu)^{2} / 2 \sigma^{2}} d X$$
In Equation (3.53) the variable $X$ is the generic variable, and the lower-case $x$ represents a particular value.

The logistic model, $\operatorname{CDF}(x)=F(x)=P(X \leq x)=\frac{1}{1+e^{-s(x-c)}}$, is a convenient and reasonably good approximation to the normal $C D F(x)$. Convenient: It is computationally simple, analytically invertible, and analytically differentiable. Reasonably good: Values are no more different from the normal CDF $(x)$ than that caused by uncertainty on $\mu$ and $\sigma$. For the scale factor, use $s=\sigma / 1.7$, and for the center, use $c=\mu$ (see Exercise 3.15).

## 统计代写|工程统计作业代写Engineering Statistics代考|Continuous Distributions

pdF(X)=一种和−一种X,0≤X≤∞,一种>0

F(X)=1−和−一种X

μ=1一种

σ2=1一种2

40%=0.40=F(吨)=1−和−一种吨=1−和−一种(24)

## 统计代写|工程统计作业代写Engineering Statistics代考|Gamma Distribution

pdF(X)=λΓ(一种)(λX)一种−1经验⁡(−λX),X≥0

Γ(一种)=∫0∞从一种−1和−和d从

Γ(一种)=(一种−1)Γ(一种−1)

Γ(一种)=(一种−1)!

μ=一种λ σ2=一种λ2

## 统计代写|工程统计作业代写Engineering Statistics代考|Normal Distribution

F(X)=1σ2圆周率和[−12(X−μσ)2],−∞<X<∞

CDF⁡(X)=F(X)=磷(X≤X)=1σ2圆周率∫−∞X和−(X−μ)2/2σ2dX

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|工程统计作业代写Engineering Statistics代考|Continuous Distributions

statistics-lab™ 为您的留学生涯保驾护航 在代写工程统计Engineering Statistics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写工程统计Engineering Statistics代写方面经验极为丰富，各种代写工程统计Engineering Statistics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|工程统计作业代写Engineering Statistics代考|Continuous Distributions

In the previous section, the distributions were related to the number count of events. In contrast, many measurements are continuum-valued. Continuous distributions model the probabilities associated with continuous variables, such as those that describe events such as service life, pressure drop, flow rate, temperature, percent conversion, and degradation in yield strength.

That we measure continuous variables in discrete units or at fixed time intervals does not matter; the variables themselves are continuous even if the measuring devices give data that are recorded as if step changes had occurred. A familiar example is body temperature, a continuous variable measured in discrete increments. Think about it: Even if you have a fever, your temperature does not change from $98.6$ to $101.2^{\circ} \mathrm{F}$ in one step or even in a series of connected $0.2^{\circ} \mathrm{F}$ intervals, just because the thermometer is calibrated that way.
We must acknowledge, however, that the world is not continuous. From an atomic and quantum mechanical view of the universe, no event has a continuum of values. However, on the macroscale of engineering, individual atoms are not distinguishable within measurement discrimination, and so the world appears continuous. For most practical engineering purposes, it is possible to approximate any distribution in which the discrete

variable has more than 100 values with a probability density function of a continuous random variable.
A cumulative continuous distribution function $F(x)$ is defined as
$$C D F(x)=F(x)=\int_{-\infty}^{x} p d f(X) d X$$
where $p d f(X)$ is a continuous probability density function and $X$ is a continuous variable, which could represent time, temperature, weight, composition, etc. $x$ is a particular value of the variable $X$. The units on $x$ and $X$ are identical and are not a count of the number of events as the $x$-variable in the discrete distributions. The $F(x)$ is the area under the $p d f(x)$ curve, is dimensionless, and as $x$ goes from $-\infty$ to $+\infty, F(x)$ goes from 0 to 1 .
$$\int_{-\infty}^{+\infty} p d f(X) d X=1$$
Note, again, the terms $C D F$ and $F$ are used interchangeably.
Additionally, the terms $p d f(x)$ and $f(x)$ are also used interchangeably. In the discrete distributions, $p d f(x)$ would mean point distribution function, and in continuous functions, it means probability density function.

Although both the continuum $p d f(x)$ and discrete $f\left(x_{i}\right)$ represent the histogram shape of data, they are different. The dimensional units of $p d f(x)$ constitute a major difference between a continuous probability distribution function and the $f\left(x_{i}\right)$ of a discrete point probability distribution. The $p d f(x)$ necessarily has dimensional units that are the reciprocal of the continuous variable. For $F(x)$ of Equation (3.31) to be dimensionless, integrating with $d x$, the argument of the integral, $p d f(x)$, must have the units of the reciprocal of $d x$. $p d f(x)$ is often termed a rate, a rate of change of $F(x)$ w.r.t. $x$. By contrast, in a discrete function $F\left(x_{i}\right)$ is the sum of $f\left(x_{i}\right)$, the fraction of the dataset with a value of $x_{j}$, so $f\left(x_{i}\right)$ is dimensionless. You cannot use a discrete point distribution in Equation (3.31) or a continuous function in Equation (3.1) and expect $F(x)$ to remain a dimensionless cumulative probability. Another difference between discrete and continuous probability density functions is that $x$ is used only to represent values of the variable involved throughout the continuous case. For discrete distributions, $x$ was often the number of events in a particular class (category).
So, whether you are using the term $p d f(x)$ or $f(x)$ take care that you are properly using the dimensionless version for distributions of a discrete variable, and the rate version with reciprocal units of $X$ for distributions of continuum variables.
The mean and variance of the theoretical continuum distributions are:
$$\begin{gathered} \mu=\int_{-\infty}^{+\infty} x p d f(x) d x \ \sigma^{2}=\int_{-\infty}^{+\infty}(x-\mu)^{2} p d f(x) d x \end{gathered}$$

## 统计代写|工程统计作业代写Engineering Statistics代考|Continuous Uniform Distribution

If a random variable can have any numerical value within the range from $a$ to $b$ and no values outside that range, and if each possible value has an equal probability of occurring, then the probability density function for the uniform continuous distribution is

The random variable $X$ may have any dimensional units which must match that of parameters $a$ and $b$. The mean, $\mu$ will have the same units. Whereas the cumulative distribution function $F(x)$ is dimensionless, the probability density function, $p d f(x)$, has units that are the reciprocal of those of the random variable $X$.

Again, the population coefficients, $a$ and $b$, represent the true values. You might not know what they are exactly, but certainly you can do enough experiments to get good estimates for them.

## 统计代写|工程统计作业代写Engineering Statistics代考|Proportion

A proportion is the probability of an event, a fraction of outcomes, and is a continuumvalued variable. In flipping a coin, the probability of a particular outcome is $p=0.5$. In rolling a die the probability of getting a 5 is $p=0.166 \overline{66}$. In rolling 10 dice and winning means getting at least one five in the 10 outcomes, the probability is $p=0.83949441$…. Although the events are discrete, the probability could have a continuum of values between 0 and 1. $0 \leq p \leq 1$.

If the proportion is developed theoretically, then it is known with as much certainty as the basis and idealizations allow. Then the variance on the proportion is 0 .
$$\sigma_{p}^{2}=0$$
Alternately, the proportion could be determined from experimental data. For example, a trick die could be weighted to have $p=0.21$ as the probability of rolling a 5 . Here, proportion, $p$, is the ratio of number of successes, s, per total number of trials, $n, p=s / n$, as $n \rightarrow \infty$. Alternately, the proportion would be estimated as the average after many trials.
$$\hat{\mu}{p}=\hat{p}=\frac{s}{n}=\frac{\sum s{i}}{\sum n_{i}}$$
If experimentally determined, the variance on the proportion would be estimated by
$$\hat{\sigma}_{p}{ }^{2}=\frac{\hat{p}(1-\hat{p})}{n}=\frac{\hat{p} \hat{q}}{n}=\frac{s(n-s)}{n^{3}}$$
Note this is similar to the mean and variance of the binomial distribution, but here the statistics are on the continuum-valued proportion. In the binomial distribution, the statistics

are on the number count of a particular type of event. The variance of the count of successes of $n$ samples from a population would be given by Equation (3.14).
Example 3.9: What are the mean and sigma when the probability of an event (outcome $=1$ ) is and unknown $p$, and the probability of a not-an-event (outcome $=0$ ) is $q=(1-p)$ ? A sequence of $n$ dichotomous events might be
$$0,0,1,1,1,0,1,0,0,1,0,0,1, \ldots$$
Whether we call the event a $\mathrm{H}$ or a $\mathrm{T}$, a success or a fail, the ${1,0}$ notation is equivalent. Experimentally, there are $s=21$ successes out of $n=143$ trials. From Equation (3.40) the estimate of $p$ is
$$\hat{p}=\frac{s}{n}=\frac{21}{143}=0.14685314 \ldots$$
From Equation (3.41) the standard deviation on $\hat{p}$ is
$$\hat{\sigma}{p}=\sqrt{\hat{\sigma}{p}^{2}}=\sqrt{\frac{s(n-s)}{n^{3}}}=\sqrt{\frac{21(143-21)}{143^{3}}}=0.02959957 \ldots$$
acknowledging the uncertainty on $\hat{p}$ and $\hat{\sigma}{p}$ one might report $$\hat{p}=0.148$$ and $$\hat{\sigma}{p}=0.03$$

## 统计代写|工程统计作业代写Engineering Statistics代考|Continuous Distributions

variable 有超过 100 个值，具有连续随机变量的概率密度函数。

CDF(X)=F(X)=∫−∞XpdF(X)dX

∫−∞+∞pdF(X)dX=1

μ=∫−∞+∞XpdF(X)dX σ2=∫−∞+∞(X−μ)2pdF(X)dX

## 统计代写|工程统计作业代写Engineering Statistics代考|Proportion

σp2=0

μ^p=p^=sn=∑s一世∑n一世

σ^p2=p^(1−p^)n=p^q^n=s(n−s)n3

0,0,1,1,1,0,1,0,0,1,0,0,1,…

p^=sn=21143=0.14685314…

σ^p=σ^p2=s(n−s)n3=21(143−21)1433=0.02959957…

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|工程统计作业代写Engineering Statistics代考|Poisson Distribution

statistics-lab™ 为您的留学生涯保驾护航 在代写工程统计Engineering Statistics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写工程统计Engineering Statistics代写方面经验极为丰富，各种代写工程统计Engineering Statistics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|工程统计作业代写Engineering Statistics代考|Poisson Distribution

The Poisson distribution is concerned with the number of events occurring during a given time or space interval. The interval may be of any duration or in any specified region. The Poisson distribution, then, can be used to describe the number of breaks or other flaws in a particular beam of finished cloth, or the arrival rate of people in a queuing line, or the number of defectives in a paint weathering trial, or the number of defective beakers per line per shift. The Poisson distribution describes processes with the following properties:

1. The number of events, $X$, in any time interval or region is independent of those occurring elsewhere in time or space.
2. The probability of an event happening in a very short time interval or in a very small region does not depend on the events outside this interval or region.
3. The interval or region is so short or small that the number of events in the interval is much smaller than the total number of events, $n$.
The point Poisson distribution (point probability) function $f(x)$ can be expressed as
$$f(x)=\frac{\lambda^{x} e^{-\lambda}}{x !}$$
where $x$ is the number of events, $f(x)$ is the probability of $x$ events occurring in an interval, $\lambda$ is the expected average number of events per interval, and $e=2.7182818 \ldots$ is the base of the natural logarithm system.
The cumulative Poisson distribution function $F(x)$ is
$$C D F(x)=F(x)=P(X \leq x)=\sum_{k=0}^{x} \frac{\lambda^{k} e^{-\lambda}}{k !}$$
where $e$ is the base of the natural logarithm system.

## 统计代写|工程统计作业代写Engineering Statistics代考|Negative Binomial Distribution

In cases in which the binomial distribution governs the probability of occurrence of one of two mutually exclusive events, we calculated the probability of success exactly $s$ times out of $n$ trials. The negative binomial distribution is used in a complementary way, that is, for calculating the probability that exactly $n$ trials are required to produce $s$ successes. The probabilities of success and failure remain fixed at $p$ and $q$, respectively. The only way this situation can occur is for exactly $(s-1)$ of the first $(n-1)$ trials to be a success, and for the next, or last, trial also to be a success. The probability of $x=n$, the number of trials needed to produce $s$ successful outcomes, then
$$f(x=n \mid s)=\left(\begin{array}{c} n-1 \ s-1 \end{array}\right) p^{s} q^{n-s}, s \leq n$$
is the negative binomial distribution. The cumulative negative binomial distribution is
$$F(x=n \mid s)=P(s \leq x \leq n)=\sum_{i=s}^{n}\left(\begin{array}{c} i-1 \ s-1 \end{array}\right) p^{s} q^{i-s}$$
Figure $3.4$ illustrates the negative binomial distribution for $p=0.5$ and $s=3$. The mean and variance of the negative binomial distribution are given by
$$\mu=\frac{s}{p}$$

and
$$\sigma^{2}=\frac{s q}{p^{2}}$$
The units on $x, s, n$, and $\mu$ are the numbers of trials. The point and cumulative distribution functions, $f\left(x_{i}\right)$ and $F\left(x_{i}\right)$, are dimensionless. The units on $p$ and $q$ are the probabilities of success or failure.
Example 3.5: Suppose one of your power sources for an analytical instrument in the quality control laboratory has died with a snap and a wisp of smoke. You have finally located the trouble as a faulty integrated circuit (IC). You have been able to find five replacement ICs. You have also found that for this service the chance of failure of an IC is $12 \%$. What is the probability that you will have to use all five ICs before getting one that does not burn out?

Let us define burnout as failure, so $q=0.12$ and $p=0.88$. As $x=5$ and $s=1$, using Equation (3.19),
$$f(x=5 \mid 1)=\left(\begin{array}{l} 4 \ 0 \end{array}\right)(0.88) 0.12^{4}=1.825 \times 10^{-4} \text { or } 0.02 \%$$
the probability is less than $0.02 \%$ that you will have to try all five of the ICs to repair the power supply.

## 统计代写|工程统计作业代写Engineering Statistics代考|Hypergeometric Distribution

The hypergeometric distribution is often used to obtain probabilities when sampling is done without replacement. As a result, the probability of success changes with each trial or experiment. The point hypergeometric probability function is
$$P(X=s)=f(s)=\frac{\left(\begin{array}{l} S \ s \end{array}\right)\left(\begin{array}{c} N-S \ n-s \end{array}\right)}{\left(\begin{array}{l} N \ n \end{array}\right)}, s \leq \min (n, S)$$
where $N$ is the population size, $n$ is the sample size, $S$ is the actual number of successes in the population, $s$ is the number of successes in the sample, and $n \leq N$ and $(n-s) \leq(N-S)$. The cumulative hypergeometric distribution is
$$F(x)=P(X \leq x)=\sum_{k=0}^{x} \frac{\left(\begin{array}{l} S \ k \end{array}\right)\left(\begin{array}{c} N-S \ n-k \end{array}\right)}{\left(\begin{array}{c} N \ n \end{array}\right)}$$
Examples of the point and cumulative hypergeometric distributions are shown in Figure $3.5$ for $N=20, S=15$, and $n=5$.
The mean of the point hypergeometric distribution is
$$\mu=\frac{n S}{N}$$

and the variance is
$$\sigma^{2}=\frac{N-n}{N-1} n \frac{S}{N} \frac{N-S}{N}$$
The units of $\mu, s, N, n$, and $S$ are the number of items, populations, or successes. The point and cumulative probability functions $f(x)$ and $F(x)$ are dimensionless.
Example 3.6: In the production of avionics equipment for civilian and military use, one manufacturer randomly inspects $10 \%$ of all incoming parts for defects. If any of the parts is defective, all the rest are inspected. If 2 of the next box of 50 diodes are actually defective, what is the probability that all of the diodes will be checked before use? This question is really whether the quality control sample of 5 will contain at least one of the defective parts.
For this problem, $N=50, n=5$, and $\mathrm{s}=2$, as we choose to define success as finding a defective diode. The probability is found from
\begin{aligned} F(0) &=P(X \geq 1)=\sum_{k=1}^{2} \frac{\left(\begin{array}{c} 2 \ k \end{array}\right)\left(\begin{array}{c} 50-2 \ 5-k \end{array}\right)}{\left(\begin{array}{c} 50 \ 5 \end{array}\right)} \ &=0.1918367 \text { or } 19 \% \end{aligned}
With the current sampling procedure, there is approximately a $20 \%$ chance of finding a defective part.

## 统计代写|工程统计作业代写Engineering Statistics代考|Poisson Distribution

1. 事件的数量，X，在任何时间间隔或区域中，独立于在时间或空间其他地方发生的那些。
2. 在很短的时间间隔或很小的区域内发生事件的概率不取决于该间隔或区域之外的事件。
3. 区间或区域太短或太小，以至于区间内的事件数远小于事件总数，n.
点泊松分布（点概率）函数F(X)可以表示为
F(X)=λX和−λX!
在哪里X是事件的数量，F(X)是概率X间隔内发生的事件，λ是每个间隔的预期平均事件数，并且和=2.7182818…是自然对数系统的底。
累积泊松分布函数F(X)是
CDF(X)=F(X)=磷(X≤X)=∑ķ=0Xλķ和−λķ!
在哪里和是自然对数系统的底。

## 统计代写|工程统计作业代写Engineering Statistics代考|Negative Binomial Distribution

F(X=n∣s)=(n−1 s−1)psqn−s,s≤n

F(X=n∣s)=磷(s≤X≤n)=∑一世=sn(一世−1 s−1)psq一世−s

μ=sp

σ2=sqp2

F(X=5∣1)=(4 0)(0.88)0.124=1.825×10−4 或者 0.02%

## 统计代写|工程统计作业代写Engineering Statistics代考|Hypergeometric Distribution

F(X)=磷(X≤X)=∑ķ=0X(小号 ķ)(ñ−小号 n−ķ)(ñ n)

μ=n小号ñ

σ2=ñ−nñ−1n小号ññ−小号ñ

F(0)=磷(X≥1)=∑ķ=12(2 ķ)(50−2 5−ķ)(50 5) =0.1918367 或者 19%

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|工程统计作业代写Engineering Statistics代考|Discrete Distributions

statistics-lab™ 为您的留学生涯保驾护航 在代写工程统计Engineering Statistics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写工程统计Engineering Statistics代写方面经验极为丰富，各种代写工程统计Engineering Statistics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|工程统计作业代写Engineering Statistics代考|Discrete Distributions

There are two classes of distributions: Discrete and continuous. Discrete distributions are used to describe data that can have only discrete values. Such data have a specific probability associated with each value of the random variable. There are distinct and measurable step changes associated with each value of the variable. Some examples of discrete variables are the size of the last raise you received (it was not in fractions of a cent), the score of the last sporting event you watched, the number of personal protective equipment items available to you on your job, the number of first-quality computer chips on a silicon wafer, the number of defects in a skein of yarn, the energy of electrons in a particular quantum state, the number of raindrops that fall onto a square inch of land, etc.

The variable $x_{i}$ represents the count of events in the $i$ th category. The categories are mutually exclusive, such as alphabet letters, or pass/fail. The value of $x_{i}$ is an integer number. Looking at this paragraph, if $I=1$ represents the occurrence of the letter “a” and $I=2$ that of the letter ” $\mathrm{b}$ “, then the value of $x_{1}=18$ and $x_{2}=4$.

Probability density functions, $p d f\left(x_{i}\right)$ or simply $f\left(x_{i}\right)$, are associated with distributions of discrete variables, $x_{i}$ represent the probability of possible values of the ith data category. For example, if you flip a coin you expect $k=2$, two outcomes, Head and Tail, or 0 and 1 . If the first classification of $x_{1}=$ Head, then $f\left(x_{1}\right)=0.5$. All such probability functions have the following properties:

1. $x_{i}$ are the discrete possible values of a variable $X$, and $x_{\mathrm{i}}$ is the $i$ th of the $k$ finite values of the outcome. Usually, the index $i$ places the $x_{i}$ values in ascending order.
2. The probability functions are mathematical models of the population, of the infinity of possible samples, not of a finite sample of $k$ number of values.
3. $f\left(x_{i}\right)$ is the frequency, the probability of occurrence that a value $x_{i}$ will occur. It is positive and real for each $x_{\dot{r}} f\left(x_{i}\right)=\lim {n \rightarrow \infty}\left{n{i} / n\right}$.
4. $\sum_{i=1}^{k} f\left(x_{i}\right)=1$ where $k$ is the number of categories.
5. $P(E)=\sum f\left(x_{i}\right)$ where the sum includes all $x_{i}$ in the event $E$.
These definitions illustrate the notation we use throughout this book. We use capital Latin letters for populations and lowercase Latin letters for particular numerical observation values from the populations. Lowercase Greek letters are used for population parameters. Point and cumulative distributions are identified by $f$ and $F$ (or alternately CDF) respectively. $P$ stands for “probability of …”. We are using the conventional notation for discrete distributions: $x$ in the summations of the cumulative distribution functions of discrete distributions sometimes represents the number of items in a class (group, collection, etc.) or at other times, $x$ represents the numerical value that quantifies the class. By using this notation, the formulas in this book are consistent with those you may find in other statistics books. We state this as a warning, because in conventional notation for variables, $x$ means the value of the variable as opposed to the number of occurrences in a category. The cumulative distribution function (CDF) is a function $F\left(x_{n}\right)$ obtained from the probability function and is defined for the values of $x_{i}$ of the random variable $X$ by
$$F\left(x_{r}\right)=F\left(x_{r}\right)=P\left(X \leq x_{r}\right)= \begin{cases}0 & \text { for } X<x_{1} \ \sum_{i=1}^{r} f\left(x_{i}\right) & \text { where } x_{1} \leq X \leq x \ 1 & \text { for } X \geq x_{n}\end{cases}$$

## 统计代写|工程统计作业代写Engineering Statistics代考|Discrete Uniform Distribution

When each discrete event has the same likelihood (probability) of occurring, the probability function is given by
$$f\left(x_{i}\right)=\frac{1}{n}, \quad 1 \leq i<n$$
where $n$ is the number of discrete values for $x$. For the cumulative discrete distribution function,
$$F\left(x_{i}\right)=P\left(X \leq x_{i}\right)=\frac{i}{n}$$
where $x_{1}<x_{2}<x_{3} \ldots<x_{n}$
A classic example is that of rolling a cubical die. The $n=6$ categories of possible outcomes are equally probable.

The $X$ in Equation (3.6) may represent either a dimensionless counting number ( 7 bolts), a category ( 3 Heads) or a dimensional real number (last raise was $\$ 437.25 / \mathrm{month}$); however,$X$must be limited to a finite number,$n$, of discrete values. For the raise example, the discrete values are multiples of$1 \mathrm{c} / \mathrm{month}$. If the maximum possible raise could have been$\$600.00 /$ month, then $n=600.00 / .01+1=60,001$ (we cannot exclude the zero-raise event). Consequently, $x_{10,000}$ represents the 10,000 th value of $X$, which is $\$ 99.99 / \mathrm{mon}$th. Figure$3.1$illustrates the discrete uniform distribution for$n=5$, and the corresponding cumulative discrete uniform distribution, also for$n=5$. Recognizing that each$x_{i}$value has the same probability, or frequency of occurring,$f\left(x_{i}\right)=f\left(x_{j}\right)$, the mean and variance of the discrete uniform distribution are $$\begin{gathered} \mu=\frac{1}{n} \sum_{i=1}^{n} x_{i} \ \sigma^{2}=\frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-\mu\right)^{2} \end{gathered}$$ If the$x_{i}$values are also equally incremented between$x_{1}=a$and$x_{n}=b$, so that$x_{j+1}-x_{j}=\Delta x=(b-a) / n$(such as with a die which has sides with values of$1,2,3 \ldots, 6$, where$a=1$and$b=6$) then ## 统计代写|工程统计作业代写Engineering Statistics代考|Binomial Distribution A discrete distribution called the binomial occurs when any observation can be placed in only one of two mutually exclusive categories, such as greater-than or less-than-or-equalto, safe or unsafe, hot or cold, on or off, 0 or 1, pass or fail, Heads or Tails, etc. Although these characteristics are qualitative, the distribution can be made quantitative by assigning the values 0 and 1 to the two categories. The method of assignment is immaterial so long as it is consistent. Customarily, the categories are labeled success (value$=1$) and failure (value$=0$). If$p=$probability of success and$q=1-p=$probability of failure in one trial of the experiment (one observation), the probability of exactly$x$number of successes in$n$trials can be described by the corresponding term of the binomial expansion, or $$f(x \mid n)=\left(\begin{array}{l} n \ x \end{array}\right) p^{x} q^{n-x} \equiv \frac{n !}{x !(n-x) !} p^{x} q^{n-x}, x=0,1,2, \ldots, n$$ where$X$may only have integer values. Note: The$\left(\begin{array}{l}n \ x\end{array}\right)$symbol does not mean$n$divided by$x$, it represents$\frac{n !}{x !(n-x) !}$, which is the number of combinations (ways) of having$x$occur in$n$trials. If$n=4$and$x=2$then$\left(\begin{array}{l}n \ x\end{array}\right)=\frac{4 !}{2 !(4-2) !}=\frac{4 \times 3 \times 2 \times 1}{2 \times 1(2 \times 1)}=6$. The six possible success-fail patterns could be 1100,1010 , 1001, 0110, 0101, and$0011 .$Note: The variable$x$represents the numerical count in a particular category, it is not the value of the category. Note: When$n$is large, the factorial terms become large, and direct calculation of either the numerator or denominator can result in digital overflow. Fortunately, the number of integers in the numerator and denominator is equal, there are$n$digits in each, and a best way to calculate the ratio is to alternate dividing and multiplying. But, many software packages provide convenient functions. In Excel the function is$f(x \mid n)=\operatorname{BINOMIAL} \cdot \mathrm{DIST}(x, n, p, 0)$. The binomial cumulative distribution function is $$F\left(x_{i} \mid n\right)=P\left(X \leq x_{i} \mid n\right)=\sum_{k=0}^{x_{i}}\left(\begin{array}{l} n \ k \end{array}\right) p^{k}(1-p)^{n-k}, i=0,1,2, \ldots, n$$ where$X$may have only integer values, for selected values of$n$and$p$. The notation (something$\mid n)$means “something given the value of$n^{\prime \prime}$. In Excel$F\left(x_{i} \mid n\right)=\operatorname{BINOMIAL}$.DIST$(x, n, p, 1)$. One can compute other probabilities such as$P\left(x_{i} \leq X \leq x_{i}\right)$, indicating the probability that an observation value,$X$, would be between and including$x_{i}$and$x_{\dot{r}}$$$P\left(x_{i} \leq X \leq x_{j}\right)=P\left(X \leq x_{j}\right)-P\left(X \leq x_{i-1}\right)=F\left(x_{j}\right)-F\left(x_{i-1}\right)$$ The best way to explain the use of Equation (3.11) is by use of a brief example. If you want$P(10 \leq X \leq 20)$, you need to exclude all values of$X$which are not in the probability specification. In this case, we want to include only the values$X=10,11,12, \ldots, 20$. The values of$X=0,1,2, \ldots, 9$must be excluded. As$x_{1}=10$, to exclude values below 10 , we must use$\left(x_{1}-1\right)=(10-1)=9$as the index. Specific values, such that the probability will be exactly$s$successes in$n$trials, can be found from $$P(X=s \mid n)=P(X \leq s \mid n)-P(X \leq(s-1) \mid n)$$ ## 工程统计代写 ## 统计代写|工程统计作业代写Engineering Statistics代考|Discrete Distributions 有两类分布：离散和连续。离散分布用于描述只能具有离散值的数据。这样的数据具有与随机变量的每个值相关联的特定概率。变量的每个值都存在明显且可测量的阶跃变化。离散变量的一些例子是你上一次加薪的大小（不是几分之一）、你最后一次观看体育赛事的分数、你在工作中可用的个人防护装备数量、硅晶片上第一质量的计算机芯片的数量，一束纱线中的缺陷数量，特定量子态的电子能量，落在一平方英寸土地上的雨滴数量等。 变量X一世表示事件的计数一世类别。类别是互斥的，例如字母或通过/失败。的价值X一世是一个整数。看这一段，如果一世=1表示字母“a”的出现和一世=2那封信”b“，那么值X1=18和X2=4. 概率密度函数，pdF(X一世)或者干脆F(X一世)，与离散变量的分布相关，X一世表示第 i 个数据类别的可能值的概率。例如，如果你掷硬币，你期望ķ=2，两个结果，头和尾，或 0 和 1。如果第一个分类X1=头，然后F(X1)=0.5. 所有这些概率函数都具有以下性质： 1. X一世是变量的离散可能值X， 和X一世是个一世的第ķ结果的有限值。通常，索引一世将X一世值按升序排列。 2. 概率函数是总体的数学模型，是无限可能样本的数学模型，而不是有限样本的数学模型。ķ值的数量。 3. F(X一世)是频率，一个值出现的概率X一世会发生。对于每个$x_{\dot{r}} f\left(x_{i}\right)=\lim {n \rightarrow \infty}\left{n {i} / n\right}$都是正实数. 4. ∑一世=1ķF(X一世)=1在哪里ķ是类别的数量。 5. 磷(和)=∑F(X一世)其中总和包括所有X一世在事件中和. 这些定义说明了我们在本书中使用的符号。我们使用大写拉丁字母表示总体，使用小写拉丁字母表示来自总体的特定数值观测值。小写希腊字母用于人口参数。点分布和累积分布由F和F（或交替CDF）分别。磷代表“……的概率”。我们对离散分布使用传统表示法：X在离散分布的累积分布函数的总和中有时表示一个类（组、集合等）或其他时候的项目数，X表示量化类的数值。通过使用这种表示法，本书中的公式与您在其他统计书籍中可能找到的公式是一致的。我们将此声明为警告，因为在变量的传统表示法中，X表示变量的值，而不是类别中的出现次数。累积分布函数 (CDF) 是一个函数F(Xn)从概率函数获得并定义为X一世随机变量X经过 F(Xr)=F(Xr)=磷(X≤Xr)={0 为了 X<X1 ∑一世=1rF(X一世) 在哪里 X1≤X≤X 1 为了 X≥Xn ## 统计代写|工程统计作业代写Engineering Statistics代考|Discrete Uniform Distribution 当每个离散事件具有相同的发生可能性（概率）时，概率函数由下式给出 F(X一世)=1n,1≤一世<n 在哪里n是离散值的数量X. 对于累积离散分布函数， F(X一世)=磷(X≤X一世)=一世n 在哪里X1<X2<X3…<Xn 一个典型的例子是掷骰子。这n=6可能结果的类别同样可能。 这X等式 (3.6) 中的数字可以表示无量纲计数（7 个螺栓）、类别（3 个 Heads）或有量纲实数（最后一次提升是$437.25/米这n吨H); 然而，X必须限制在一个有限的数量，n, 离散值。对于 raise 示例，离散值是1C/米这n吨H. 如果最大可能的加薪可能是$600.00/月，然后n=600.00/.01+1=60,001（我们不能排除零加注事件）。最后，X10,000代表第 10,000 个值X，即$99.99/米这nth。

μ=1n∑一世=1nX一世 σ2=1n∑一世=1n(X一世−μ)2

## 统计代写|工程统计作业代写Engineering Statistics代考|Binomial Distribution

F(X∣n)=(n X)pXqn−X≡n!X!(n−X)!pXqn−X,X=0,1,2,…,n

F(X一世∣n)=磷(X≤X一世∣n)=∑ķ=0X一世(n ķ)pķ(1−p)n−ķ,一世=0,1,2,…,n

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|工程统计作业代写Engineering Statistics代考|Bayes’ Belief Calculations

statistics-lab™ 为您的留学生涯保驾护航 在代写工程统计Engineering Statistics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写工程统计Engineering Statistics代写方面经验极为丰富，各种代写工程统计Engineering Statistics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|工程统计作业代写Engineering Statistics代考|Bayes’ Belief Calculations

Belief is the confidence that you have in making a statement of fact about something, a supposition. Here are some examples of statements that we might make:

“These symptoms are just seasonal allergies.”
“The average benefit of Treatment $Y$ is larger than that of Treatment $X$.”
“The process has reached steady-state.”
And for each we might claim to be very certain of the supposition (perhaps $99 \%$ sure), or somewhat certain (perhaps $80 \%$ sure), or even not sure whether it is or is not (perhaps $50 \%$ sure).

Bayes’ Belief, $B$, is scaled by $100 \%$, so the value is $0 \leq B \leq 1$. If you are not so certain about a statement, the belief, $B$, might be $0.25$. If you are very certain, $B$ might be $0.97$. If you are not so sure about something, and it could be a $50 / 50$ call, then $B=0.5$.

Because we act on suppositions, we want to be fairly certain that the statement about what we suppose represents the truth about the reality. When you are not certain, you perform tests, take samples, get other’s opinions, etc. to strengthen or to reject your belief in the supposition. But tests are not perfect. There is always some uncertainty about the results. For example, the manufacturer of a particular procedure for detecting the presence of colorectal cancer reports it detects the disease in $92 \%$ of the patients with cancer and gives a negative result in $87 \%$ of the patients without the disease. (Exact Sciences Laboratories, Cologuard Patient Guide, 2020). The $92 \%$ correct positives means $8 \%$ false negatives. (The test on $8 \%$ of patients with the disease will falsely indicate they do not have it.) Similarly, the $87 \%$ correct negatives means $13 \%$ false positives. (The test on $13 \%$ of patients without the disease will falsely indicate they have it.)
Table $2.1$ is a matrix of the probabilities of the medical test giving true and false indications.

Here is another example: A test for steady-state (SS) might look at the past several data points. At SS the time-rate of change, data slope, ideally is zero, $S=0$. But, because of noise on the data, the slope will not be exactly zero; so, you might accept SS if the test results are $-0.1 \leq S \leq+0.1$. So, if the test result indicates $S=-0.03$ you say that is just noise, and the test indicates SS. But, at SS, a particular confluence of data perturbations might indicate the local slope is $S=0.15$, and the test would reject the true condition of SS. Maybe, given a true SS, the test will indicate SS $85 \%$ of the time, and reject SS $15 \%$ of the time.

On the other hand, if the process is in a transient state (TS), the slope will be much greater than a SS value, the slope will be beyond the $-0.1 \leq S \leq+0.1$ limits, and the test result will claim TS. However, even in a TS when the process variable is rising, the noise pattern on the past few samples might have a decreasing pattern, and the rate of change might incorrectly indicate SS. Maybe, given a true TS, the test will indicate TS $95 \%$ of the time, and SS 5\%.

## 统计代写|工程统计作业代写Engineering Statistics代考|Takeaway

1. In flipping a fair coin twice, what is the probability of a) getting two Heads, b) getting two Tails, c) getting a Head on the first flip and a Tail on the second, d) not getting any Heads?
2. At a particular summer camp, the probability of getting a case of poison ivy is $0.15$ and the probability of getting sunburn is $0.45$. What is the probability of a) neither, b) both, c) only sunburn, d) only poison ivy?
3. After rolling three fair six-sided dice, what is the probability of a) getting three ones showing, b) having only one four showing, c) getting a one and a two and a three?
4. If the probability of rain tomorrow is $70 \%$ and rain the next day is $50 \%$, then $0 \%$ for the next five days, what is the probability of rain a) on both of the next two days, b) on all of the next seven days, c) at least once this week?
5. There are two safety systems on a process. If an over-pressure event happens in the process, the first safety override should quench the source, and if that is not adequate the back-up system should release excess gas to a vent system. Normal control of the process is generally adequate, only permitting an average of about ten over-pressure events per year. The quench system, we are told, has a $95 \%$ probability of working adequately when needed, and the back-up vent has a $98 \%$ probability of working as needed. What is the probability of an undesired event (the over-pressure happens, and it is not contained by either safety system) in a) the next one-year period, and b) the next ten-year period?
6. There is a belief that Treatment B is better than the current Treatment A in use. The belief is a modest $75 \%, B=0.75$. If $\mathrm{B}$ is equivalent to $\mathrm{A}$, not better, then there is a $50 / 50$ chance that the trial outcome will indicate either B is better or worse. However, if B is better, then the chance that it will appear better in the trial is $80 \%$. What is the new belief after the trial if a) the trial indicates B is better, b) if the trial indicates $B$ is not better, and c) how many trials of sequential successes are needed to make the belief that $B$ is the right choice raise to $99 \%$ ?
7. A restaurant buys thousands of jalapeno peppers per day, of which $5 \%$ are not spicy-hot. They use five peppers in each small batch of salsa. If two (or more) of the five are not hot, customers are likely to complain that the salsa is not adequate. What is the probability of making an inadequate batch of salsa? Quantify how larger batch sizes will change the probability.

## 统计代写|工程统计作业代写Engineering Statistics代考|Definitions

Measurement: A numerical value indicating the extent, intensity, or measure of a characteristic of an object.

Data: Either singular as a single measurement (such as a $y$-value) or plural as a set of measurements (such as all the $y$-values). Data could refer to an input-output pair $(x, y)$ or the set $(x, y)$.
Observation: A recording of information on some characteristic of an object. Usually a paired set of measurements.

Sample: 1) A subset of possible results of a process that generates data. 2) A single observation.
Sample size: The number of observations, datasets, in the sample.
Population: All of the possible data from an event or process – usually $n=\infty$.
Random disturbance: Small influences on a process that are neither correlated to other variables nor correlated to their own prior values.

Random variable: A variable or function with values that are affected by many independent and random disturbances despite efforts to prevent such occurrences.

Discrete variable: A variable that can assume only isolated values, that is, values in a finite or countably infinite set. It may be the counting numbers, or it may be the digital display values of truncated data.

Continuum variable: A variable that can assume any value between two distinct numbers.
Frequency: The fraction of the number of observations within a specified range of numerical values relative to the total number of observations.

Cumulative frequency: The sum of the frequencies of all values less than or equal to a particular value.

Mean: A measure of location that provides information regarding the central value or point about which all members of the random variable $X$ are distributed. The mean of any distribution is a parameter denoted by the Greek letter $\mu$.

Variance: A parameter that measures the variability of individual population values $x_{i}$ about the population mean $\mu$. The population variance is indicated by $\sigma^{2}$.
Standard deviation: $\sigma$ is the positive square root of the variance.
Empirical Distributions: These are obtained from a sampling of the population data. As a result, the models or the parameter values that best fit a model to the data (such as $\mu$ and $\sigma$ ) may not exactly match those of the population.

Theoretical Distributions: These are obtained by derivation from concepts about the population. If the concepts are true, then the models and corresponding parameter values represent the population. But nature is not required to comply with human mental constructs.
Category (classification): The name of a grouping of like data, influences, events such as heads, defectives, zero-crossings, integers, negative numbers, green, etc.

## 统计代写|工程统计作业代写Engineering Statistics代考|Bayes’ Belief Calculations

“这些症状只是季节性过敏。”
“治疗的平均收益是大于治疗的X。”
“这个过程已经达到稳定状态。”

## 统计代写|工程统计作业代写Engineering Statistics代考|Takeaway

1. 抛一个公平的硬币两次，a) 得到两个正面，b) 得到两个反面，c) 第一次得到正面，第二次得到反面，d) 没有得到正面的概率是多少？
2. 在一个特定的夏令营中，得到一箱毒藤的概率是0.15晒伤的概率是0.45. a) 两者都没有，b) 两者都有，c) 只有晒伤，d) 只有毒藤的概率是多少？
3. 在掷出三个公平的六面骰子后，a) 得到三个 1，b) 只有一个 4，c) 得到 1 和 2 和 3 的概率是多少？
4. 如果明天下雨的概率是70%第二天下雨50%， 然后0%在接下来的 5 天里，a) 在接下来的两天中，b) 在接下来的所有 7 天中，c) 本周至少一次下雨的概率是多少？
5. 一个过程有两个安全系统。如果过程中发生过压事件，第一个安全超控应熄灭源，如果这还不够，备用系统应将多余的气体释放到排气系统。该过程的正常控制通常是足够的，每年仅允许平均约十次过压事件。我们被告知，淬火系统有一个95%在需要时充分工作的可能性，并且备用通风口具有98%根据需要工作的可能性。在 a) 下一个一年期和 b) 下一个十年期中发生意外事件（发生过压，并且两个安全系统均未包含）的概率是多少？
6. 有一种观点认为治疗 B 优于当前使用的治疗 A。信念是谦虚的75%,乙=0.75. 如果乙相当于一种，不是更好，那么有一个50/50试验结果表明 B 更好或更差的可能性。但是，如果 B 更好，那么它在试验中看起来更好的机会是80%. 如果 a) 试验表明 B 更好，b) 如果试验表明，试验后的新信念是什么乙不是更好，并且 c) 需要多少次连续成功的试验才能使人们相信乙是正确的选择99% ?
7. 一家餐馆每天购买数千个墨西哥胡椒，其中5%不辣。他们在每小批莎莎酱中使用五个辣椒。如果五个中的两个（或更多）不热，客户可能会抱怨莎莎酱不够。制作不足批次的莎莎酱的概率是多少？量化更大的批量将如何改变概率。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|工程统计作业代写Engineering Statistics代考|Probability

statistics-lab™ 为您的留学生涯保驾护航 在代写工程统计Engineering Statistics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写工程统计Engineering Statistics代写方面经验极为丰富，各种代写工程统计Engineering Statistics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|工程统计作业代写Engineering Statistics代考|Probability

An event is a particular outcome of a trial, test, experiment, or process. It is a particular category for the outcome. You define that category.

The outcome category could be dichotomous, meaning either one thing or another. In flipping a coin, the outcome is either a Head (H) or a Tail (T). In flipping an electric light switch to the “on” position, the result is either the light lights or it does not. In passing people on a walk, they either return the smile or do not. These events are mutually exclusive, meaning if one happens the other cannot. You could define the event as a $\mathrm{H}$, or as a T; as the light working, or the light not working.

Alternately, there could be any number of mutually exclusive events. If the outcome is one event, one possible outcome from all possible discrete outcomes, then it cannot be any other. The event of randomly sampling the alphabet could result in 26 possible outcomes. But if the event is defined as finding the letter ” $\mathrm{T}^{\prime \prime}$, this success excludes finding any of the other 25 letters.

By contrast, the outcome may be a continuum-valued variable, such as temperature, and the event might be defined as sampling a temperature with a value above $85^{\circ} \mathrm{F}$. A temperature of $84.9^{\circ} \mathrm{F}$ would not count as the event. A temperature of $85.1^{\circ} \mathrm{F}$ would count as the event. For continuum-valued variables, do not define an event as a particular value. If the event is defined as sampling a temperature value of $85^{\circ} \mathrm{F}$, then $84.9999999^{\circ} \mathrm{F}$ would not count as the event. Nor would $85.00000001^{\circ} \mathrm{F}$ count as the event. Mathematically, since a point has no width, the likelihood of getting an exact numerical value, is impossible. So, for continuum-valued outcomes, define an event as being greater than, or less than a particular value, or as being between two values.

One definition of probability is the ratio of the number of particular occurrences of event to the number of all possible occurrences of mutually exclusive events. This classical definition of probability requires that the total number of independent trials of the experiment be infinite. This definition is often not as useful as the relative-frequency definition. That interpretation of probability requires only that the experiment be repeated a finite number of times, $n$. Then, if an event $E$ occurs $n_{E}$ times out of $n$ trials and if the ratio $n_{E} / n$ tends to stabilize at some constant as $n$ becomes larger, the probability of $E$ is denoted as:
$$P(E)=\lim {n \rightarrow \infty} n{E} / n$$
The probability is a number between 0 and 1 and inclusive of the extremes 0 and 1 , $0 \leq P(E) \leq 1$.

## 统计代写|工程统计作业代写Engineering Statistics代考|A Priori Probability Calculations

Let us consider that $E_{1}$ and $E_{2}$ are two user-specified events (results) of outcomes of an experiment. Here are some definitions:

If $E_{1}$ and $E_{2}$ are the only possible outcomes of the experiment, then the collection of events $E_{1}$ and $E_{2}$ is said to be exhaustive. For instance, if $E_{1}$ is that the product meets specifications and $E_{2}$ is that the product does not meet specifications, then the collection $E_{1}$ and $E_{2}$ represents all possible outcomes and is exhaustive.

The events $E_{1}$ and $E_{2}$ are mutually exclusive if the occurrence of one event precludes the occurrence of the other event. For example, again, if $E_{1}$ is that the product meets specifications and $E_{2}$ is that the product does not meet specifications, then $E_{1}$ precludes $E_{2}$, they are mutually exclusive, if the outcome is one, then it cannot be the other.

Event $E_{1}$ is independent of event $E_{2}$ if the probability of occurrence of $E_{1}$ is not affected by $E_{2}$ and vice versa. For example, flip a coin and roll a die. The coin flip event of being a Head is independent of the number that the die roll reveals. As another example, $E_{1}$ might be that the product meets specifications, and $E_{2}$ might be that fewer than two employees called in sick. These are independent.

The composite event ” $E_{1}$ and $E_{2} “$ means that both events occur. For example, you flipped a $\mathrm{H}$ and rolled a 3. If the events are mutually exclusive, then the probability that both can occur is zero.

The composite event ” $E_{1}$ or $E_{2}^{\prime \prime}$ means that at least one of events $E_{1}$ and $E_{2}$ occurs. When you flipped and rolled, a H and/or a 3 were the outcomes. This situation allows both $E_{1}$ and $E_{2}$ to occur but does not require that result, as does the ” $E_{1}$ and $E_{2}{ }^{\prime \prime}$ case.
There could be any number of user-specified events, $E_{1}, E_{2}, E_{3}, \ldots, E_{n}{ }^{\circ}$ Two rules govern the calculation of a priori probabilities.

## 统计代写|工程统计作业代写Engineering Statistics代考|Conditional Probability Calculations

In some cases, an event has happened and we wish to determine the probability a posteriori (after the fact) that a particular set of circumstances existed based on the results already obtained. Suppose that several factors $B_{i}, i=1, n$ can affect the outcome of a specific situation or event, $E$. The probability that any of the $B_{i}$ did occur, given that the event or outcome $E$ has already occurred, is a conditional probability. Let’s begin with the premise that $B_{1}, B_{2}, B_{3}$, and $B_{4}$ can influence $E$, an event that has happened. The final event $E$ can take place only if at least one of the preliminary events (the $B_{i}$ ) has already happened. The probability that a particular one of them, e.g., $B_{3}$ occurred is $P\left(B_{3} \mid E\right)$. If one of the $B_{i y}$ say $B_{3}$, had to happen for $E$ to transpire, then $B_{3}$ is conditional on $E$.
These are end-of-process events and beginning-of-process conditions.
Conditional probabilities can be determined by the use of Bayes’ theorem. Bayes’ theorem is stated in Equation (2.10), where $P\left(B_{i}\right)$ and $P\left(B_{k}\right)$ are the a priori probabilities of the occurrences of events $B_{i}$ and $B_{k}$ and $P\left(B_{i} \mid E\right)$ and $P\left(B_{k} \mid E\right)$ are the conditional probabilities that $B_{i}$ or $B_{k}$ would occur if event $E$ has already occurred.
$$P\left(B_{k} \mid E\right)=\frac{P\left(B_{k}\right) P\left(E \mid B_{k}\right)}{n}$$
Here:

1. $E$ is an event, an outcome.
2. $B$ is a condition (a situation, or an influence).
3. $P(B)$ is the probability of a condition happening.
4. $P(E \mid B)$ is the probability $E$ occurring given that $B$ did.
5. $P(E) \cdot P(E \mid B)$ is the probability $B$ and it caused $E$.
6. $\Sigma$ is the sum of all probabilities of all ways that $E$ could happen.
7. $P(B \mid E)$ is the probability $B$ happening given that $E$ did.

## 统计代写|工程统计作业代写Engineering Statistics代考|Conditional Probability Calculations

1. 和是一个事件，一个结果。
2. 乙是一种条件（情况或影响）。
3. 磷(乙)是某种情况发生的概率。
4. 磷(和∣乙)是概率和鉴于发生乙做过。
5. 磷(和)⋅磷(和∣乙)是概率乙它导致和.
6. Σ是所有方式的所有概率的总和和可能发生。
7. 磷(乙∣和)是概率乙鉴于发生和做过。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|工程统计作业代写Engineering Statistics代考|Uses of Statistics

statistics-lab™ 为您的留学生涯保驾护航 在代写工程统计Engineering Statistics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写工程统计Engineering Statistics代写方面经验极为丰富，各种代写工程统计Engineering Statistics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|工程统计作业代写Engineering Statistics代考|Uses of Statistics

You will use statistics in five ways. One is in the design of experiments or surveys. In this instance, you need the answers to some questions about an event or a process. An effective experiment is one that has been designed so that the answers to your questions will be obtained more often than not. An efficient experiment is one that is unbiased (predicts

the correct value of the parameter) and that also has the smallest variance (scatter about the true value of the population parameter in question). Efficiency also means that the answers will have been obtained with the minimum expenditure of time (yours, an operator’s, a technician’s, etc.) and other resources.

The second way you will use statistical techniques is with descriptive statistics. This method involves using sample data to make an inference about the population. The population is the entire or complete set of possible values, attributes, etc. that are common to, describe, or are characteristic of a given experiment or event. A sample is a subset of that data. Descriptive statistics are used for describing and summarizing experimental, production, reliability, and other types of data.

The description can take many forms. The average, median, and mode are all measures of centrality. Variance, standard deviation, and probable range are all measures variation. The descriptor may be a probability, which refers to the chance an event might happen (such as getting three or more successes in five-coin flips) or the chance that a value might exceed some threshold (the probability of seeing someone taller than $6 \mathrm{ft} 8$ in on your next shopping trip).

It is essential that your samples are random samples if you are to have any reasonable expectation of obtaining reliable answers to your questions. To obtain a random sample, you must first define, not just describe, the population under consideration. Then you can use the principles of random selection of population values or experimental conditions to obtain the random sample that is essential to statistical inference.

A third statistical use is estimating the uncertainty of a value, estimating the possible range of values it might have. The value might be an average from a sample and the question is what range of population means could have generated that sample average. The value might be a predicted outcome from a model when all model coefficient values and influences are not known with certainty.

A fourth use of statistics is in the testing of hypotheses. A hypothesis about any event, process, or variable relationship is a statement of anticipated behavior under specified conditions. Hypotheses are tested by determining whether the hypothesized results reasonably agree with the observed data. If they do, the hypothesis is likely to be valid. Otherwise, the hypothesis is likely to be false. Hypotheses could be relatively complex, such as the model matching the data, the design being reliable, or the process being at steady-state.

The fifth use of methods in this book is to obtain quantitative relationships between variables by use of sample data. This aspect of statistics is loosely called “curve fitting” but is more properly termed regression analysis. We will use the method of least squares for regression because that technique provides a conventional way to estimate the “best fit” of the data to the hypothetical relationship.

## 统计代写|工程统计作业代写Engineering Statistics代考|Stationarity

In statistics, a stationary process does not change in mean (average) or variance (variability). It is steady, but any measurement is subject to random variation. The value of the data perturbation changes from sample to sample, but the distribution of the perturbations does not change.

This is in contrast to classic deterministic analysis of transient and steady-state processes. A steady process flatlines in time. The measurement achieves a particular value

and remains at that value. When the process is in a transient state the average or mean changes in time.

In statistics the term stationary means that the steady-state process will not deterministically flatline. Instead, the data will be continually fluctuating about a fixed value (mean) with the same variance. In statistics, a stationary process is not in a transient state.

Level of confidence is a measure of how probable your statistical conclusion is. As an example, after testing raw materials A and B for their influence on product purity, you might be $95 \%$ confident that A leads to higher purity. But you cannot extend this result to report that you are $95 \%$ sure that using raw material A is the better business decision. You have only tested product purity. You have not evaluated product variability, other product characteristics, manufacturing costs, process safety implications, etc. You can only be $95 \%$ confident in your evaluation of purity. Be careful that you do not project statistical confidence about one aspect onto your interpretation of the appropriate business action.

## 统计代写|工程统计作业代写Engineering Statistics代考|Correlation is Not Causation

Statistics does not prove that some event or value caused some other response. Causation refers to a cause-and-effect mechanism. Correlation means that there is a strong relationship between two variables, or observations.

As an example, there is a strong correlation to people awakening and the sun rising, but one cannot claim that people awakening causes the sun to rise. The cause-and-effect mechanism for this observed correlation is more akin to the opposite. As another example,

there is a strong correlation between gray hair and wrinkles, but that does not mean that gray hair causes wrinkles. The mechanism is that another variable, age, causes both observations.

So, more so than just tempering claims about confidence in taking action from testing a single aspect, be careful not to let indications of correlation dupe you into claiming causation. If you have an opinion as to the cause-and-effect mechanism, and you have correlation that supports it, before you claim it is the truth, perform experiments and seek data that could reject your hypothesized mechanism. State exactly, mechanistically how the treatment leads to the outcome expectations. State what else you expect should be observed, and what should not be observed. State when and where these should be observed. Do the experiments to see if your hypothesized theory is true.

Traditionally, statistics deals with the probable outcomes from a distribution. This book is grounded in that mathematical science, and many examples reveal how to describe the likelihood of some extreme value.

But more than this, the basis (the “givens”) in any particular application have uncertainty, which is unlike the basis of givens in a schoolbook example. In the real world, to make decisions based on the statistical analysis, the impact of uncertainty needs to be considered. Further, concerns over possible negative choices might not just be about monetary shortfalls. They may be related to disparate issues such as reputation.

This book includes a chapter on propagation of uncertainty, another on stochastic simulation, and frequent discussions on Equal-Concern approaches for combining disparate metrics.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|工程统计作业代写Engineering Statistics代考|Fundamentals of Probability and Statistics

statistics-lab™ 为您的留学生涯保驾护航 在代写工程统计Engineering Statistics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写工程统计Engineering Statistics代写方面经验极为丰富，各种代写工程统计Engineering Statistics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|工程统计作业代写Engineering Statistics代考|Introduction

In this book, the word statistics is used in two ways. First, it refers to the techniques involved in collecting, analyzing, and drawing conclusions from data – a procedure, or a recipe. The second, more frequently inferred meaning, is that of an estimated value, a number, calculated from either the data or a proposed theory, that is used for comparative purposes in testing a hypothesis (guess, supposition, etc.) about a parameter of a population – a numerical value. The topics presented in this book have been selected from our experience (and others’) to provide you with a set of procedures which are relevant to application work (such as data analysis in engineering, science, and business). Although fundamental concepts are explained and some equations are derived, the focus of this book is on the how-to of statistical applications.

There is a tension between perfection and sufficiency. Perfection seeks the truth, which follows the mathematical science viewpoint. Although perfection provides grounding in statistical analysis methods, it is usually a mathematical analysis that is predicated on many idealizations, making it imperfect. By contrast, sufficiency seeks utility and functional adequacy, a balance of expediency which is also grounded in mathematical fundamentals. Sufficiency is not sloppiness or inaccuracy. It is appropriate liberty with the idealization, grounded in an understanding of the limitations of the idealization and uncertainty in the “givens”. Both perfection and sufficiency are important, and perspectives of both are presented in this text. In this “Applied Engineering” text the balance tends toward sufficiency, rather than unrealistic perfection.

## 统计代写|工程统计作业代写Engineering Statistics代考|Deterministic and Stochastic

The term deterministic means that there is no uncertainty, there is perfect certainty about a value. Here are some simple examples: What is 3 times 4 ? Given that the side of a cube is $2.1 \mathrm{~cm}$, what is the surface area? What angle (rounded to three digits) has a tangent value of $0.75$ ? These were very simple calculations, but it is the same with something more complicated, such as: Given a particular heat exchanger and fluid flow rates and associated properties, use the equations in your heat transfer book to calculate the exit temperatures of the fluids. Regardless of the time of day, or location, or the computer type being used, every time the calculation is performed, we get exactly the same answer.

The term stochastic means that we get a different answer each time the calculation is performed, or each time the measurement is obtained. Here are some examples: What is the height of the next person you pass on the street? How many grains of sand are in a handful? If the product label indicates that the package contains $40 \mathrm{lbs}$, what might be the actual weight? If there are the same number of red and green marbles in a box and you draw three, blindfolded, how many green marbles will you have? If you want to compare fertilizer treatments, you will find that the year-to-year variation in weather and insect population, and the location-to-location variation in properties of the earth will cause significant variation in results.

Despite the use of deterministic calculations in teaching concepts and in estimating values, the reality about measurements and samples and predictions is that they have variation. Statistics provides techniques for analyzing and making decisions within the uncertainty.
Sources of variation include the vagaries of weather, the probability of selecting a particular sample, variation in raw material, mechanical vibration, incomplete fluid mixing, prior stress on a device, new laws and regulations, future prices, and many other aspects.

## 统计代写|工程统计作业代写Engineering Statistics代考|Treatments, Process, and Outcomes

The term treatment refers to the influence on a process. The influence might be how safety training is delivered (video, reading materials, in-person, comically, or seriously). A treatment could be a recipe or procedure to be followed. A treatment could be the type of equipment used (batch or continuous, toaster or microwave). A treatment could be the raw material supplier or the service provider. The treatment might be the operating conditions in manufacturing (flow rates, temperatures, mixing time, etc.).

The process is whatever responds to the treatment. It may be a human response to an office lighting treatment. It may be a mechanical spring-and-weight response to treatment by the ambient temperature. It may be a biological process response to a $\mathrm{pH}$ (acidity) treatment.

Outcome refers to the response of the process. It may be the time to recover physical health after an infection in response to the medicine dose. It may be the economic response of the nation due to changes in the prime lending rate. It may be the variation in a quality metric due to a particular treatment. It may be the probability of automobile accidents if the speed limit is changed.

Treatments and outcomes are variously termed influences and responses, causes and effects, inputs and outputs, independent and dependent variables, etc.

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。