数学代写|概率论代写Probability theory代考|STAT4028

statistics-lab™ 为您的留学生涯保驾护航 在代写概率论Probability theory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。我们的专家在代写概率论Probability theory代写方面经验极为丰富，各种代写概率论Probability theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

数学代写|概率论代写Probability theory代考|Random trial, sample space, and event

Consider a trial with an unknown prior result, yet known possible results. Such a trial is called a random trial, and the set of its possible results is called sample space, usually denoted by the letter $S$. For more clarification, consider the following examples:
In the trial of tossing one coin, the sample space is as follows:
$$S={H, T}^1$$
In the trial of tossing two coins, the sample space is defined as:
$$S={(H, H),(T, H),(H, T),(T, T)}$$

In the trial of tossing two dice, the sample space consists of 36 states and is defined as:
$$S={(i, j): i, j=1,2,3,4,5,6}$$
In the trial of measuring the lifetime of a particular light bulb (in hours), the sample space is defined as:
$$S={x: x \geq 0}$$
Each subset of a sample space with possible outcomes belonging to a trial is called the sample space event.

For instance, consider the trial of tossing two coins. If the event $E$ denotes at least one heads appears, the event is expressed as follows:
$$E={(H, T),(T, H),(H, H)}$$
Alternatively, consider the trial of tossing two dice. If the event $E$ denotes the sum of the results of two dice is equal to 4 , the event is expressed as:
$$E={(1,3),(2,2),(3,1)}$$
Also, in the trial of measuring the lifetime of a particular light bulb, the event $E$ is defined as the lifetime of the light bulb with a maximum value of 10 hours. This event is represented as follows:
$$E={x: 0 \leq x \leq 10}$$
Note that we say the event $E$ has occurred when one of its results has occurred. Namely, in the trial of tossing two dice, assume that the event $E$ denotes the sum of the results of two dice is equal to 4 . Then, if one of the results $(1,3),(2,2)$, or $(3,1)$ occurs, we say that the event $E$ has occurred.

数学代写|概率论代写Probability theory代考|An introduction to the algebra of sets

In the probability theory, the algebra of sets and the relationships between different Levents of a trial are of great importance, which are addressed in this section. Meanwhile, we assume that all the studied events belong to one sample space such as S.

One illustrative method to indicate the logical relationships of events is the use of the Venn Diagram. In this diagram, the sample space of the trial is represented by a rectangle containing all the points, and the various events such as $\mathrm{E}$ and $\mathrm{F}$ are usually shown as circles inside the rectangle. Thus, the desired events can be shown by hatching the related area of the figure.

If $\mathrm{E}$ and $\mathrm{F}$ are arbitrary two events of the sample space, then we say that $E \cap F$ or $E F$ is the intersection of two cvents $E$ and $F$. That is, it contains all possible results of the trial, which are both in the events E and F.

In fact, $E \cap F$ occurs whenever both of the events $\mathrm{E}$ and $\mathrm{F}$ occur. For this purpose, a result of the sample space should occur that is in common for both of the events.

Moreover, we say that $E \cup F$ is the union of two events $E$ and $F$ whenever it contains all results either in $\mathrm{E}$ or $\mathrm{F}$ (or both), as shown Figure $2-1$.

In other words, $E \cup F$ occurs whenever at least one of the events $E$ and $F$ occurs. To this end, a result of the sample space should occur that is either in $E$ or $F$ (or both), shown as $E \cup F$.

Namely, in the trial of tossing a die, suppose that the events $E$ and $F$ are defined as $E={1,2,3}$ and $F={3,4}$, respectively. Then, the events $E \cap F$ and $E \cup F$ will lead to the respective values ${3}$ and ${1,2,3,4}$.

概率论代考

数学代写|概率论代写Probability theory代考|Random trial, sample space, and event

$$S=H, T^1$$

$$S=(H, H),(T, H),(H, T),(T, T)$$

$$S=(i, j): i, j=1,2,3,4,5,6$$

$$S=x: x \geq 0$$

$$E=(H, T),(T, H),(H, H)$$

$$E=(1,3),(2,2),(3,1)$$

$$E=x: 0 \leq x \leq 10$$

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。

数学代写|概率论代写Probability theory代考|STAT4528

statistics-lab™ 为您的留学生涯保驾护航 在代写概率论Probability theory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。我们的专家在代写概率论Probability theory代写方面经验极为丰富，各种代写概率论Probability theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

数学代写|概率论代写Probability theory代考|Combinations

suppose that we have ” $n$ ” distinct objects. The number of states of choosing ” $r$ ” distinct objects from these ” $n$ ” distinct objects (without considering the order of choices) is equal to:
$$C_r^n=\left(\begin{array}{l} n \ r \end{array}\right)=\frac{n !}{(n-r) ! \times(r !)}$$
To prove the above equation, it suffices to refer to one of the similar previous problems with a straightforward answer. The number of states of selecting ” $r$ ” distinct objects from ” $n$ ” distinct objects with consideration of their permutations (orders) is $P_r^n=\frac{n !}{(n-r) !}$, every $r !$ results of which are equivalent to one state of the new problem (selecting objects without consideration of the permutations). For instance, in choosing a three-member group from a ten-member group of people, every 3 ! states of the problem with consideration of the order of choices are equivalent to one state of the problem without consideration of the order of choices.

Therefore, the number of states that we can choose three of the seven distinct elements equals:
$$C_3^7=\left(\begin{array}{l} 7 \ 3 \end{array}\right)=\frac{P_3^7}{3 !}=\frac{7 !}{4 ! 3 !}$$
Likewise, in general, it can be shown that the number of states of choosing ” $r$ ” elements from the ” $n$ ” distinct elements is equal to:
$$C_r^n=\frac{P_r^n}{r !}=\frac{n !}{(n-r) ! r !}=\frac{(n)(n-1) \cdots(n-(r-1))}{r !}=\left(\begin{array}{l} n \ r \end{array}\right)$$

Suppose that a class consists of five boys and four girls.
a) How many ways can a group of size 3 be chosen from them?
b) How many ways can a group of size 3 consisting of one girl and two boys be chosen?
c) How many ways can a group of size 3 consisting of at most one boy be chosen?

数学代写|概率论代写Probability theory代考|Significant identities of the combinatorial topic

in this section, we are about to introduce some of the widely used combinatorial identities in the probability theory and prove them analytically. The first identity is as follows:
$$\left(\begin{array}{l} n \ r \end{array}\right)=\left(\begin{array}{c} n \ n-r \end{array}\right) ; \quad 0 \leq r \leq n$$
To prove it analytically, suppose we have an $n$-member set and we want to select ” $r$ ” members from them (left side of the identity). Such a selection can be made by firstly choosing $(n-r)$ members of the set, setting them aside (right side of the identity), and then regarding the remaining $r$ members as the leading members of the set.

The second combinatorial identity known as the Pascal’s identity is expressed as follows:
$$\left(\begin{array}{l} n \ r \end{array}\right)=\left(\begin{array}{c} n-1 \ r-1 \end{array}\right)+\left(\begin{array}{c} n-1 \ r \end{array}\right) ; \quad 1 \leq r \leq n$$
Consider an $n$-member set and suppose that we want to select ” $r$ ” members from the set (left side of the identity). To do so, regard a specific element such as “A” and divide all the possible states into two groups. The first group consists of the states in which the member ” $\mathrm{A}$ ” is among the ” $r$ ” members selected, and the second group consists of states in which the member ” $\mathrm{A}$ ” is not among the ” $r$ ” members selected (right side of the identity). The number of possible states in which the member “A” is selected equals $\left(\begin{array}{l}1 \ 1\end{array}\right)\left(\begin{array}{l}n-1 \ r-1\end{array}\right)$, and the number of possible states in which the member ” $\mathrm{A}$ ” is not selected equals $\left(\begin{array}{l}1 \ 0\end{array}\right)\left(\begin{array}{c}n-1 \ r\end{array}\right)$. Hence, the total number of states is equal to:
$$\left(\begin{array}{l} 1 \ 0 \end{array}\right)\left(\begin{array}{c} n-1 \ r \end{array}\right)+\left(\begin{array}{l} 1 \ 1 \end{array}\right)\left(\begin{array}{l} n-1 \ r-1 \end{array}\right)=\left(\begin{array}{c} n-1 \ r \end{array}\right)+\left(\begin{array}{l} n-1 \ r-1 \end{array}\right)$$

概率论代考

数学代写|概率论代写Probability theory代考|Combinations

$$C_r^n=(n r)=\frac{n !}{(n-r) ! \times(r !)}$$

$$C_3^7=(73)=\frac{P_3^7}{3 !}=\frac{7 !}{4 ! 3 !}$$

$$C_r^n=\frac{P_r^n}{r !}=\frac{n !}{(n-r) ! r !}=\frac{(n)(n-1) \cdots(n-(r-1))}{r !}=(n r)$$

a) 有多少种方法可以从中选出一组大小为 3 的方法?
b) 一组由一个女孩和两个男孩组成的大小为 3 的小组有多少种选择?
c) 最多由一个男孩组成的 3 人组有多少种选择?

数学代写|概率论代写Probability theory代考|Significant identities of the combinatorial topic

$$(n r)=(n n-r) ; \quad 0 \leq r \leq n$$

$$(n r)=(n-1 r-1)+(n-1 r) ; \quad 1 \leq r \leq n$$

$$(10)(n-1 r)+(11)(n-1 r-1)=(n-1 r)+(n-1 r-1)$$

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。

数学代写|概率论代写Probability theory代考|STAT4061

statistics-lab™ 为您的留学生涯保驾护航 在代写概率论Probability theory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。我们的专家在代写概率论Probability theory代写方面经验极为丰富，各种代写概率论Probability theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

数学代写|概率论代写Probability theory代考|The Basic Principle of Counting

Il methods of counting rely on the Basic Principle of Counting or the Principle of Multiplication, which is expressed as follows:

Suppose that two trials are to be done. If the first trial can obtain one out of the $n$ possible results and each of those results correspond with the $m$ possible results of the second trial, then altogether there are $n \times m$ possible results for performing the two trials.

A noteworthy point in applying the multiplication principle is to pay attention to the phrase “each of those results”. Even though it seems obvious, many mistakes occurring in usage of the multiplication principle result from disregarding the very point. Note the following examples:

There are 12 coaches, each of whom has 4 athletes participating in a ceremony. If one coach and one of his athletes are to be chosen as the coach and athlete of the year, respectively, how many different choices are possible to do so?

Solution. We define the first and second trials to be choosing the coach and athlete of the year, respectively. The first trial can be done in 12 states, and given the selection of each coach in the first trial, choosing his athlete can be done in 4 states. Hence, the trials can be performed in $12 \times 4=48$ states.

Suppose that five coaches have two athletes each and the other seven coaches have three athletes each. Now, if we want to choose one coach and one of his athletes as the coach and athlete of the year, how many different choices are possible to do so?

Solution. Since given some of the results of the first trial (choosing coaches), there are two rcsults for the sccond trial (choosing athletes). Also, given some other results of the first trial, there are three possible results for the second trial. Hence, we cannot directly use the principle of counting. In such situations, we should divide the problem into two different parts and, concerning the principle of multiplication, count the number of states belonging to each part. Then, by using the Principle of Plus (the additional plus), we will add up the number of states of each part. Consequently, the answer to this example equals $5 \times 2+7 \times 3=31$.

Generally, if there are $n_2$ results for each of the $n_1$ results of the first trial and $m_2$ results for each of the $m_1$ results of the second trial, then these two trials can be done in $n_1 n_2+m_1 m_2$ states altogether.

数学代写|概率论代写Probability theory代考|Permutation of ” n ” distinct elements at a round table

The number of states that ” $n$ ” distinct elements can be arranged at a round table is equal to $(n-1)$ !. To prove it, we should know that the only difference between the problem of arranging people at a round table and in a row is that the location of people does not matter in the former case, which the only important point is the way of arranging the people. We are now trying to establish a relationship between the number of states of this problem and the number of states of seating people in a row. Also, it is intended to show that every ” $n$ ” states of seating people in a row are equivalent to one state of seating people at a round table.

As mentioned previously, in the problem of arranging people at a round table, the only important issue is the order of sitting. Hence, the states shown below are considered indistinguishable: Therefore, there is a relationship between the states of seating people in a row and at a round table as follows:

Hence, the number of states of seating people at a round table can be written as follows:
The number of states of seating n people at a round table $=($ The number of states of seating $n$ people in a row $) \times \frac{1}{n}=n ! \times \frac{1}{n}=(n-1)$ !
There is also another way to justify the formula of arranging people around a round table. Since different possible places of the round table do not create a new state for the first person, there is only one state for him. However, after he sits, since the way of sitting relative to the first person is important for the other ones, the value of places turns out to be different, and the number of states of seating them relative to the first person equals:
$$1 \times(n-1) \times(n-2) \times(n-3) \times \ldots \times 1=(n-1) !$$

How many ways can ” $n$ ” people be seated at a round table such that person A sits between person $B$ and person $C$ ?

Solution 1. There is one state for person A. Then, there are two states for person B to sit on the left or right side of the person A. In this status, there is one state for person C. Finally, the other $(n-3)$ people can sit on the remaining places in $(n-3)$ ! states. Therefore, the number of states equals:
$$1 \times 2 \times 1 \times(n-3) !=2 \times(n-3) !$$

概率论代考

数学代写|概率论代写Probability theory代考|The Basic Principle of Counting

II 计数方法依赖于计数基本原理或乘法原理，其表达如下:

数学代写|概率论代写Probability theory代考|Permutation of ” n ” distinct elements at a round table

$$1 \times(n-1) \times(n-2) \times(n-3) \times \ldots \times 1=(n-1) !$$

$$1 \times 2 \times 1 \times(n-3) !=2 \times(n-3) !$$

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。

数学代写|概率论代写Probability theory代考|MAST20006

statistics-lab™ 为您的留学生涯保驾护航 在代写概率论Probability theory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。我们的专家在代写概率论Probability theory代写方面经验极为丰富，各种代写概率论Probability theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

数学代写|概率论代写Probability theory代考|Abundance of Compact Subsets

First we cite a theorem from [Bishop and Bridges 1985] that guarantees an abundance of compact subsets.

Theorem 3.1.1. Abundance of compact sets. Let $f: K \rightarrow R$ be a continuous function on a compact metric space $(K, d)$ with domain $(f)=K$. Then, for all but countably many real numbers $\alpha>\inf _K f$, the set
$$(f \leq \alpha) \equiv{x \in K: f(x) \leq \alpha}$$
is compact.
Proof. See theorem (4.9) in chapter 4 of [Bishop and Bridges 1985].
Classically, the set $(f \leq \alpha)$ is compact for each $\alpha \geq \inf _K f$, without exception. Such a general theorem would, however, imply the principle of infinite search and is therefore nonconstructive. Theorem 3.1.1 is sufficient for all our purposes.

Definition 3.1.2. Convention for compact sets $(f \leq \alpha)$. We hereby adopt the convention that if the compactness of the set $(f \leq \alpha)$ is required in a discussion, compactness has been explicitly or implicitly verified, usually by proper prior selection of the constant $\alpha$, enabled by an application of Theorem 3.1.1.

The following simple corollary of Theorem 3.1.1 guarantees an abundance of compact neighborhoods of a compact set.

Corollary 3.1.3. Abundance of compact neighborhoods. Let $(S, d)$ be a locally compact metric space, and let $K$ be a compact subset of $S$. Then the subset
$$K_r \equiv(d(\cdot, K) \leq r) \equiv{x \in S: d(x, K) \leq r}$$
is compact for all but countably many $r>0$.
Proof. 1. Let $n \geq 1$ be arbitrary. Then $A_n \equiv(d(\cdot, K) \leq n)$ is a bounded set. Since $(S, d)$ is locally compact, there exists a compact set $K_n$ such that $A_n \subset K_n \subset S$. The continuous function $f$ on the compact metric space $\left(K_n, d\right)$ defined by $f \equiv$ $d(\cdot, K)$ has infimum 0 . Hence, by Theorem 3.1.1, the set $\left{x \in K_n: d(x, K) \leq r\right}$ is compact for all but countably many $r \in(0, \infty)$. In other words, there exists a countable subset $J$ of $(0, \infty)$ such that for each $r$ in the metric complement $J_c$ of $J$ in $(0, \infty)$, the set
$$\left{x \in K_n: d(x, K) \leq r\right}$$
is compact.

数学代写|概率论代写Probability theory代考|Partition of Unity

In this section, we define and construct a partition of unity relative to a binary approximation of a locally compact metric space $(S, d)$.

There are many different versions of partitions of unity in the mathematics literature, providing approximate linear bases in the analysis of various linear spaces of functions. The present version, roughly speaking, furnishes an approximate linear basis for $C(S, d)$, the space of continuous functions with compact supports on a locally compact metric space. In this version, the basis functions will be endowed with specific properties that make later applications simpler. For example, each basis function will be Lipschitz continuous.
First we prove an elementary lemma for Lipschitz continuous functions.
Lemma 3.3.1. Definition and basics for Lipschitz continuous functions. Let $(S, d)$ be an arbitrary metric space. A real-valued function $f$ on $S$ is said to be Lipschitz continuous, with Lipschitz constant $c \geq 0$, if $|f(x)-f(y)| \leq c d(x, y)$ for each $x, y \in S$. We will then also say that the function has Lipschitz constant $c$.
Let $x_{\circ} \in S$ be an arbitrary but fixed reference point. Let $f, g$ be real-valued functions with Lipschitz constants $a, b$, respectively, on $S$. Then the following conditions hold:

1. $d\left(\cdot, x_{\circ}\right)$ has Lipschitz constant 1.
2. $\alpha f+\beta g$ has Lipschitz constant $|\alpha| a+|\beta| b$ for each $\alpha, \beta \in R$. If, in addition, $|f| \leq 1$ and $|g| \leq 1$, then $f g$ has Lipschitz constant $a+b$.
3. $f \vee g$ and $f \wedge g$ have Lipschitz constant $a \vee b$.
4. $1 \wedge\left(1-c d\left(\cdot, x_{\vee}\right)\right)+$ has Lipschitz constant $c$ for each $c>0$.
5. If $|f| \vee|g| \leq 1$, then fg has Lipschitz constant $a+b$.
6. Suppose $\left(S^{\prime}, d^{\prime}\right)$ is a locally compact metric space. Suppose $f^{\prime}$ is a realvalued function on $S^{\prime}$, with Lipschitz constant $a^{\prime}>0$. Suppose $|f| \vee\left|f^{\prime}\right| \leq 1$.

概率论代考

数学代写|概率论代写Probability theory代考|Abundance of Compact Subsets

$$(f \leq \alpha) \equiv x \in K: f(x) \leq \alpha$$

Veft ${x \backslash$ in $K \ldots n: d(x, K) \backslash l e q r \backslash r i g h t}$

数学代写|概率论代写Probability theory代考|Partition of Unity

1. $d\left(\cdot, x_{\circ}\right)$ Lipschitz 常数为 1 。
2. $\alpha f+\beta g$ 有李普㳍茨常数 $|\alpha| a+|\beta| b$ 每个 $\alpha, \beta \in R$. 如果，此外， $|f| \leq 1$ 和 $|g| \leq 1$ ，然后 $f g$ 有 李普鿆茨常数 $a+b$.
3. $f \vee g$ 和 $f \wedge g$ 有李普布茨常数 $a \vee b$.
4. $1 \wedge\left(1-c d\left(\cdot, x_{\vee}\right)\right)$ +有李普㣇茨常数 $c$ 每个 $c>0$.
5. 如果 $|f| \vee|g| \leq 1$ ，那么 $f g$ 有 Lipschitz 常数 $a+b$.
6. 认为 $\left(S^{\prime}, d^{\prime}\right)$ 是局部紧度量空间。认为 $f^{\prime}$ 是一个实值函数 $S^{\prime}$, 利普布茨常数 $a^{\prime}>0$. 认为 $|f| \vee\left|f^{\prime}\right| \leq 1$

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。

数学代写|概率论代写Probability theory代考|STAT4528

statistics-lab™ 为您的留学生涯保驾护航 在代写概率论Probability theory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。我们的专家在代写概率论Probability theory代写方面经验极为丰富，各种代写概率论Probability theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

数学代写|概率论代写Probability theory代考|Notations and Conventions

Unless otherwise indicated, $N, Q$, and $R$ will denote the set of integers, the set of rational numbers in the decimal or binary system, and the set of real numbers, respectively. We will also write ${1,2, \ldots}$ for the set of positive integers. The set $R$ is equipped with the Euclidean metric $d \equiv d_{\text {ecld }}$. Suppose $a, b, a_i \in R$ for $i=m, m+1, \ldots$ for some $m \in N$. We will write $\lim {i \rightarrow \infty} a_i$ for the limit of the sequence $a_m, a{m+1}, \ldots$ if it exists, without explicitly referring to $m$. We will write $a \vee b, a \wedge b, a_{+}$, and $a_{-}$for $\max (a, b), \min (a, b), a \vee 0$, and $a \wedge 0$, respectively. The sum $\sum_{i=m}^n a_i \equiv a_m+\cdots+a_n$ is understood to be 0 if $n{n \rightarrow \infty} \sum{i=m}^n a_i$. In other words, unless otherwise specified, convergence of a series of real numbers means absolute convergence. Regarding real numbers, we quote Lemma $2.18$ from [Bishop and Bridges 1985], which will be used, extensively and without further comments, in the present book. Limited proof by contradiction of an inequality of real numbers. Let $x, y$ be real numbers such that the assumption $x>y$ implies a contradiction. Then $x \leq y$. This lemma remains valid if the relations $>$ and $\leq$ are replaced by $<$ and $\geq$, respectively.

We note, however, that if the relations $>$ and $\leq$ are replaced by $\geq$ and $<$, respectively, then the lemma would not have a constructive proof. Roughly speaking, the reason is that a constructive proof of $x0$ such that $y-x>\varepsilon$, which is more than a proof of $x \leq y$; the latter requires only a proof that $x>y$ is impossible and does not require the calculation of anything. The reader should ponder on the subtle but important difference.

数学代写|概率论代写Probability theory代考|Set, Operation, and Function

Set. In general, a set is a collection of objects equipped with an equality relation. To define a set is to specify how to construct an element of the set, and how to prove that two elements are equal. A set is also called a family.

A member $\omega$ in the collection $\Omega$ is called an element of the latter, or, in symbols, $\omega \in \Omega$.

The usual set-theoretic notations are used. Let two subsets $A$ and $B$ of a set $\Omega$ be given. We will write $A \cup B$ for the union, and $A \cap B$ or $A B$ for the intersection. We write $A \subset B$ if each member $\omega$ of $A$ is a member of $B$. We write $A \supset B$ for $B \subset A$. The set-theoretic complement of a subset $A$ of the set $\Omega$ is defined as the set ${\omega \in \Omega: \omega \in A$ implies a contradiction $}$. We write $\omega \notin A$ if $\omega \in A$ implies a contradiction.

Nonempty set. A set $\Omega$ is said to be nonempty if we can construct some element $\omega \in \Omega$.

Empty set. A set $\Omega$ is said to be empty if it is impossible to construct an element $\omega \in \Omega$. We will let $\phi$ denote an empty set.

Operation. Suppose $A, B$ are sets. A finite, step-by-step, method $X$ that produces an element $X(x) \in B$ given any $x \in A$ is called an operation from $A$ to $B$. The element $X(x)$ need not be unique. Two different applications of the operation $X$ with the same input element $x$ can produce different outputs. An example of an operation is [ [ $]_1$, which assigns to each $a \in R$ an integer $[a]_1 \in$ $(a, a+2)$. This operation is a substitute of the classical operation [·] and will be used frequently in the present work.

Function. Suppose $\Omega, \Omega^{\prime}$ are sets. Suppose $X$ is an operation that, for each $\omega$ in some nonempty subset $A$ of $\Omega$, constructs a unique member $X(\omega)$ in $\Omega^{\prime}$. Then the operation $X$ is called a function from $\Omega$ to $\Omega^{\prime}$, or simply a function on $\Omega$. The subset $A$ is called the domain of $X$. We then write $X: \Omega \rightarrow \Omega^{\prime}$, and write $\operatorname{domain}(X)$ for the set $A$. Thus a function $X$ is an operation that has the additional property that if $\omega_1=\omega_2$ in $\operatorname{domain}(X)$, then $X\left(\omega_1\right)=X\left(\omega_2\right)$ in $\Omega^{\prime}$. To specify a function $X$, we need to specify its domain as well as the operation that produces the image $X(\omega)$ from each given member $\omega$ of $\operatorname{domain}(X)$.

概率论代考

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。

数学代写|概率论代写Probability theory代考|STAT4061

statistics-lab™ 为您的留学生涯保驾护航 在代写概率论Probability theory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。我们的专家在代写概率论Probability theory代写方面经验极为丰富，各种代写概率论Probability theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

数学代写|概率论代写Probability theory代考|Natural Numbers

We start with the natural numbers as known in elementary schools. All mathematical objects are constructed from natural numbers, and every theorem is ultimately a calculation on the natural numbers. From natural numbers are constructed the integers and the rational numbers, along with the arithmetical operations, in the manner taught in elementary schools.

We claim to have a natural number only when we have provided a finite method to calculate it, i.e., to find its decimal representation. This is the fundamental difference from classical mathematics, which requires no such finite method; an infinite procedure in a proof is considered just as good in classical mathematics.
The notion of a finite natural number is so simple and so immediate that no attempt is needed to define it in even simpler terms. A few examples would suffice as clarification: 1,2 , and 3 are natural numbers. So are $9^9$ and $9^{9^9}$; the multiplication method will give, at least in principle, their decimal expansion in a finite number of steps. In contrast, the “truth value” of a particular mathematical statement is a natural number only if a finite method has been supplied that, when carried out, would prove or disprove the statement.

An algorithm or a calculation means any finite, step-by-step procedure. A mathematical object is defined when we specify the calculations that need to be done to produce this object. We say that we have proved a theorem if we have provided a step-hy-step method that translates the calculations doable in the hypothesis to a calculation in the conclusion of the theorem. The statement of the theorem is merely a summary of the algorithm contained in the proof.

Although we do not, for good reasons, write mathematical proofs in a computer language, the reader would do well to compare constructive mathematics to the development of a large computer software library, with successive objects and library functions being built from previous ones, each with a guarantee to finish in a finite number of steps.

数学代写|概率论代写Probability theory代考|Recognizing Nonconstructive Theorems

Consider the simple theorem “if $a$ is a real number, then $a \leq 0$ or $0<a$,” which may be called the principle of excluded middle for real numbers. We can see that this theorem implies the principle of infinite search by the following argument. Let $(x){i=1,2, \ldots}$ be any given sequence of 0 -or-1 integers. Define the real number $a=\sum{i=1}^{\infty} x_i 2^{-i}$. If $a \leq 0$, then all members of the given sequence are equal to 0 ; if $0<a$, then some member is equal to 1 . Thus the theorem implies the principle of infinite search, and therefore cannot have a constructive proof.

Consequently, any theorem that implies this limited principle of excluded middle cannot have a constructive proof. This observation provides a quick test to recognize certain theorems as nonconstructive. Then it raises the interesting task of examining the theorem for constructivization of a part or the whole, or the task of finding a constructive substitute of the theorem that will serve all future purposes in its stead.

For the aforementioned principle of excluded middle of real numbers, an adequate constructive substitute is the theorem “if $a$ is a real number, then, for arbitrarily small $\varepsilon>0$, we have $a<\varepsilon$ or $0<a$.” Heuristically, this is a recognition that a general real number $a$ can be computed with arbitrarily small, but nonzero, error.

We assume that the reader of this book has familiarity with calculus, real analysis, and metric spaces, as well as some rudimentary knowledge of complex analysis. These materials are presented in the first chapters of [Bishop and Bridges 1985]. We will also quote results from typical undergraduate courses in calculus or linear algebra, with the minimal constructivization wherever needed.

We assume also that the reader has had an introductory course in probability theory at the level of [Feller I 1971] or [Ross 2003]. The reader should have no difficulty in switching back and forth between constructive mathematics and classical mathematics, or at least no more than in switching back and forth between classical mathematics and computer programming. Indeed, the reader is urged to read, concurrently with this book if not before delving into it, the many classical texts in probability.

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。

数学代写|概率论代写Probability theory代考|MATHS7103

statistics-lab™ 为您的留学生涯保驾护航 在代写概率论Probability theory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。我们的专家在代写概率论Probability theory代写方面经验极为丰富，各种代写概率论Probability theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

数学代写|概率论代写Probability theory代考|THE PROBABILITY SPACE

We have considered the variants of probabilistic spaces in situations where the number of outcomes of some experiment is finite or even countable. It should be noted that such schemes are very popular. Elementary events in such situations may be, for example, the following:
“the appearance of the six when throwing a die,”
“getting a ticket with the number 7 during a random selection of 24 examination tickets,”
“three defeats of a football team before its first victory in the championship,”
“the five-time appearance of the letter “s ” on the first page of a readable newspaper,”
“the winning combination of numbers $(2,8,11,22,27,31)$ falls out in the draw of a lotttery.”
However, many experiments do not fit into these discrete schemes. For example, the result of some experiment may be the coordinate of a randomly thrown point on a real line or the coordinates of a randomly thrown point on a unit square. Therefore, a further generalization of our construction of probability spaces must be useful.

Now let $\Omega={\omega}$ be an arbitrary (not necessarily, finite or countable) set of elementary events. When moving from $\Omega$ to a set of random events, problems may arise of the type,” which combinations of elementary outcomes can be taken as elements of $F$ ?.” The examples from the previous paragraph suggest that this choice is sufficiently arbitrary. The only condition is that the elements (random events) contained in $F$ must present some kind of configurations which could be called $\sigma$-algebra. The “poorest” and very exotic will be the $\sigma$-algebra, which includes only two elements – an impossible event $\theta$ and the authentic event $\Omega$. The next in simplicity but already actually used there may be an $\sigma$-algebra composed of 4 events $A, \bar{A}, \theta$ and, where as the event $A$ one can take an arbitrary union of elementary outcomes. Naturally, to solve any specific problems we must work with some more eventful set $F$. The only condition, as already was noted, is that this set must form an $\sigma$-algebra. For example, if $\Omega$ contains all the points of the real axis, then it is convenient (but not at all necessary!) to take the Borel $\sigma$-algebra containing all segments and their various combinations.

We remind you that in any case the set $F$ must satisfy the following conditions:
1) $\Omega$ and $\theta$ must be presented in $F$;
2) if a random event $A$ is in $F$, then its addition $\bar{A}$ also belongs to $F$;
3) for any finite or countable group $A_1, A_2, \ldots$ of elements in $F$ their union $A_1 \cup A_2 \cup \ldots$ must also be contained in $F$.

数学代写|概率论代写Probability theory代考|RANDOM VARIABLES AND DISTRIBUTION FUNCTIONS

Any probabilistic space constructed is inherently a card file in which a certain set of events and a set of probabilities corresponding to them are located, which determine the degrees of opportunities for the appearance of these cerents In many cases, these prohahilitics could he found without building such heavy construction, which is a probabilistic space, but it turns out that this construction is necessary for defining and working with such important probabilistic object, which is a random variable.

The fact is that very often random outcomes of some experiment completely unrelated to any numbers or numbering can determine certain numerical characteristics depending on these outcomes.

Let’s give the simplest example. The International Football Federation (FIFA) is going to use a lot to determine where the qualifying match of the world championship between the teams of Russia and Finland will take place. The drum contains three cards with the names of the stadiums in St. Petersburg, Helsinki and the neutral field in Berlin. A randomly selected card must determine the city in which this match will take place. A fan from St. Petersburg who is going to visit this game without fail assesses his future expenses (depending on the choice of one of these three stadiums), respectively, as 3,000, 10,000 and 20,000 rubles. For him, before the draw, the future cost is a random variable, taking one of these three values with equal probabilities $1 / 3$.

Let’s consider another example. A symmetric coin must be thrown three times. The possible outcomes of this experiment are expressed in terms of the appearance of the reverse or the face in each of these three tosses:
\begin{aligned} &\omega_1={r, r, r}, \omega_2={r, r, f}, \omega_3={r, f, r}, \omega_4={f, r, r}, \ &\omega_5={r, f, f}, \omega_6={f, r, f}, \omega_7={f, f, r}, \omega_8={f, f, f} . \end{aligned}
On the set, represented by these 8 elementary outcomes, you can specify various real functions.

数学代写|概率论代写Probability theory代考|THE PROBABILITY SPACE

“掷咀子时六人的出现”、

“获胜的数字组合 $(2,8,11,22,27,31)$ 在抽签中掉出来了。”

(随机事件) 包含在 $F$ 必须呈现某种可以称为的配置 $\sigma$-代数。“最分穷”和最奇特的将是 $\sigma$-代数，它只包括两个元 素一一一个不可能的事件 $\theta$ 和真实的事件 $\Omega$. 下一个简单但已经实际使用过的可能是 $\sigma$ – 由 4 个事件组成的代数
$A, \bar{A}, \theta$ 并且，作为事件 $A$ 可以任意结合基本结果。自然，要解决任何特定问题，我们必须使用一些更重要的集 合 $F$. 正如已经提到的，唯一的条件是这个集合必须形成一个 $\sigma$-代数。例如，如果 $\Omega$ 包含实轴的所有点，那么取 Borel很方便（但完全没有必要!） $\sigma$-包含所有段及其各种组合的代数。

1) $\Omega$ 和 $\theta$ 必须呈现在 $F$;
2) 如果是随机事件 $A$ 在 $F$ ，然后它的加法 $\bar{A}$ 也属于 $F$;
3) 对于任何有限或可数群 $A_1, A_2, \ldots$ 中的元素 $F$ 他们的工会 $A_1 \cup A_2 \cup \ldots$ 也必须包含在 $F$.

数学代写|概率论代写Probability theory代考|RANDOM VARIABLES AND DISTRIBUTION FUNCTIONS

$$\omega_1=r, r, r, \omega_2=r, r, f, \omega_3=r, f, r, \omega_4=f, r, r, \quad \omega_5=r, f, f, \omega_6=f, r, f, \omega_7=f, f, r, \omega_8=f$$

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。

数学代写|概率论代写Probability theory代考|STAT4528

statistics-lab™ 为您的留学生涯保驾护航 在代写概率论Probability theory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。我们的专家在代写概率论Probability theory代写方面经验极为丰富，各种代写概率论Probability theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

数学代写|概率论代写Probability theory代考|THE SIMPLEST PROBABILISTIC MODELS

For the simplest situations, discussed before methods were proposed to rate the chances of the occurrences of events. It would be quite natural to introduce some characteristic, which makes it possible to compare the chances of the success in carrying out various experiments. Such sufficiently convenient characteristic is a certain measure of the success of the experiment (the probability of occurrence of the desired event) turned out to be the ratio $m / n$, where $n$ is the possible number of outcomes of this experiment, and $\mathrm{m}$ is the number of outcomes that suit us.

In order to consider more complex situations in which this measure of the success can be evaluated for various events of interest to us, we will try to give some scientific form to the classical model already considered before, in which this measure is determined by the ratio $m / n$.

So, we are conducting some experiment, the result of which can be (with equal chances for any of them!) $n$ outcomes. These outcomes we treat as elementary events and denote them $\omega_1, \omega_2, \ldots, \omega_n$. Thus, we define the first element of the probabilistic space – the so-called set of elementary events
$$\Omega=\left{\omega_1, \omega_2, \ldots, \omega_n\right}$$

For example, under the single throwing of a dice we have $n=6$ and $\Omega=$ $\left{\omega_1, \omega_2, \ldots, \omega_6\right}$, where $\omega_k$ means the appearance of the face with the digit $k, k=1,2,3,4,5,6$. If the coin is thrown three times, then
$$n=2^3=8, \omega_1={r, r, r}, \omega_2={r, r, f}, \ldots, \omega_8={f, f, f},$$
where the symbol ” $r$ ” corresponds to the appearance of its reverse on the first place, on the second place or on the third place, and ” $f$ ” indicates the appearance of its face during the first, second or third coin toss.

Along with the elementary situations, we may be interested in more complex outcomes of the experiment. For example, it may be important for us to have exactly an even face when throwing a dice or to get the event consisting in the appearance of at least one of three possible reverses of the coins when one deals with the throwing of three coins. What types of the cumbersome structures can be built from the original “bricks” – the elementary outcomes that we have already fixed? To construct these complex events, we can take the different groups
$$\left{\omega_{\alpha(1)}, \omega_{\alpha(2)}, \ldots, \omega_{\alpha(r)}\right}, r=1,2, \ldots, n,$$
which are composed from our “bricks.” The number of such possible groups is $C_n^1+C_n^2+\cdots+C_n^n$.

数学代写|概率论代写Probability theory代考|DISCRETE GENERALIZATIONS

In the classical probabilistic model considered above, we are dealing with $n$ outcomes of some experiment having equal chances for their appearances. The simplest examples of such classical schemes are connected, for example, with throwing of the “correct” dices or some symmetrical coins, as well as with the random selection of one or several playing cards from a well-mixed deck. However, there are substantially more situations when the possible outcomes of the carrying out experiment are not equally probable. For example, imagine that two “correct” dices are throwing, but we are interested in the sum of the readings of the two fallen faces only, then the outcomes of this experiment $\omega_2, \omega_3, \ldots, \omega_{12}$, where $\omega_k$ corresponds to the sum, which is equal to $\mathrm{k}$, no longer will be equally probable. Therefore, the first simplest generalization of the classical probability model presented above is fairly obvious.

Now let us consider the set of the elementary outcomes $\Omega=$ $\left{\omega_1, \omega_2, \ldots, \omega_n\right}$ in the case, when each outcome $\omega_k$ has its own (not necessarily equal to $1 / \mathrm{n}$ ) weight $p_k$ and the sum of all these $n$ nonnegative weights is equal to one. Then the total weight (probability)
$$P(A)=p_{\alpha(1)}+p_{\alpha(2)}+\cdots+p_{\alpha(m)}$$
corresponds to event A, which is formed from the “bricks” (elementary outcomes)
$$\left{\omega_{\alpha(1)}, \omega_{\alpha(2)}, \ldots, \omega_{\alpha(m)}\right}$$
We note that the probabilities of the impossible event and the reliable event remain equal, respectively, to zero and to one.

If we go further along the path of generalizations, we can start with the following example. Let’s return to our symmetrical coin, when the chances of falling out of the obverse or the reverse are the same and the corresponding probabilities are equal to $1 / 2$. We will now throw the coin until the appearance of the first reverse and calculate the number of obverses that fell out. It is evident that one can no longer confine ourselves to a finite number of $n$ elementary outcomes. Suppose that $\omega_k, k=0,1,2, \ldots$, is the outcome of this experiment, as a result of the situation, when a series of $k$ obverses was obtained. Note, a little ahead of the time, that the probability $p_k$, corresponding to the elementary event $\omega_k$ is equal to $1 / 2^{k+1}, k=$ $0,1,2, \ldots$

数学代写|概率论代写Probability theory代考|THE SIMPLEST PROBABILISTIC MODELS

lomega $=$ Ileft{lomega_1, lomega_2, \dots, lomega_n\right }

$$n=2^3=8, \omega_1=r, r, r, \omega_2=r, r, f, \ldots, \omega_8=f, f, f,$$

数学代写|概率论代写Probability theory代考|DISCRETE GENERALIZATIONS

$$P(A)=p_{\alpha(1)}+p_{\alpha(2)}+\cdots+p_{\alpha(m)}$$

Vleft{lomega_{lalpha(1)}, lomega_{lalpha(2)}, Vdots, lomega_{lalpha(m)}}right}

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。

数学代写|概率论代写Probability theory代考|STAT4061

statistics-lab™ 为您的留学生涯保驾护航 在代写概率论Probability theory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。我们的专家在代写概率论Probability theory代写方面经验极为丰富，各种代写概率论Probability theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

数学代写|概率论代写Probability theory代考|COMBINATORICS

In the various classical probabilistic problems very often we have to count the number of variants associated with a particular random event and to use one or another relation given above. The very origin of the theory of probahility was tied with such calculations of options associated with various combinations in gambling in which it was necessary to get the certain winning sample of cards or to get some kind of combinations favorable for the player that appear when throwing one or more dices.

Historically, the impetus to the development of the future probability theory was given in the middle of the 17 th century by some very gambler, the French knight de Mere. The history of this Chevalier de Mere is given practically in all textbooks on probability theory. The problems of this knight in 1654 were discussed at the highest scientific level, in the correspondence of Blaise Pascal, to whom de Mere addressed with his complaints, and Pierre Fermat.

Let us recall what was the reason which aroused the interest of these scientists, whose correspondence was published 25 years later in 1679 . They discussed how the odds of winning / losing are correlated in two slightly different versions of gambling, the participation in which de Mere offered to his rivals. Now any student familiar with the main principles of the probability theory would immediately help the cavalier to solve his problem, but three and a half centuries ago this problem was solved only by such outstanding scientists. Discussion of this problem led to an understanding (and the definition) of probabilities as a certain relation connecting the numbers of favourable and unfavourable outcomes of the experiment, as a result of which the corresponding event, presenting the player’s interest, may or may not appear. It is assumed that the results of this experiment can be presented by $\mathrm{n}$ equal (or, as it will be possible to qualify them later, equiprobable) outcomes. Let an event A, the appearance of which is interesting for us, occur if any of $m$ outcomes favorable to the appearance of this event is observed. Then the probability $\mathrm{P}(\mathrm{A})$ of occurrence of the event A, which is given by the equality.

This small probability to get the maximal prize does not scare a great number of the peoples who wants to become millionaires. As a result, one in about 400000 participants achieves this goal and strengthens the desire of the others to follow him. All media immediately inform us about the record wins. More recently, three Americans, buying tickets worth $\$ 2.00$each, divided the main prize in the PowerBall lottery, which amounted to about$\$$1.5 billion, for three. In this lottery, you must simultaneously guess five numbers of 69 possible white balls and one number of the 26 reds. The chances of coping with such a complex combination – one at about 292 millions. There is an interesting psychological moment. Organizers of the corresponding lottery regularly publish a set of six most frequently appearing (for all times or recently) winning numbers as well as a set of six rare numbers. Participants begin to guess, the number of which six numbers should be used in the next run. Maybe the lottery has its “favorites” and it is necessary to focus on the first six? Others object: “No! The numbers from the second six will try to overtake their colleagues from the first six. We must use them!.” As a result, the proportion of those who use numbers from these lists is increasing significantly. Since all the same random number sensors and lototrons do not react to the results of previous circulations, new winning combinations with equal chances can contain both sets of these numbers marked on the Internet, and those that did not enter into these two sixes. It should be noted in this situation that if a winning combination does contain any of these 12 specially allocated numbers, then the winnings will be divided among a significantly larger contingent of participants who have put on these combinations advertised on the Internet. Therefore, it makes sense to make six or five of the numbers that are not included in these Internet groups. Chances of the success will be the same, but the prize amount will be distributed among a smaller number of winners. Another popular probabilistic problem is connected with so-called “happy” tram, trolleybus or bus tickets. There are two classic definitions of a lucky ticket. Six-figure number makes the ticket “happy” if the sum of its first three digits coincides with the sum of the second three. Sometimes in Russia they say that this represents the “Moscow” definition of a lucky ticket, opposing to it the so-called “Leningrad” (or “St. Petersburg”) definition, which requires that the sums of three numbers on even and odd positions coincide. Both of these definitions, from the point of view of the combinatorial theory, are at least formally different, but lead to the same chances to get a lucky ticket. Suppose for completeness that in a six-digit number (a, b, c, d, e, f) in any of the six places can be any number from zero to nine, i.e., we assume the existence of a ticket whose number consists of six zeros. It is clear that the total number of possible tickets is one million exactly. Before evaluating the chances to obtain a lucky ticket, consider the following problem, the solution of which is described in detail in the classic book of N. Ya. Vylenkin [N. I. Vylenkin. Popular Combinatorics, Moscow: Nauka, 1975. 208 pp.] (See also [N. Ya. Vylenkin, AN Vilenkin, PA Vilenkin, Combinatorics, M.: FIMA, MCNMO, 2006 – 400 p.]). 概率论代考 数学代写|概率论代写Probability theory代考|COMBINATORICS 在各种经典概率问题中，我们经常必须计算与特定随机事件相关的变体数量，并使用上面给出的一种或另一种关系。概率理论的起源与赌博中与各种组合相关的选项计算相关，其中有必要获得某些获胜的纸牌样本或获得某种对玩家有利的组合，这些组合在投掷时出现或更多骰子。 从历史上看，未来概率论发展的推动力是在 17 世纪中叶由一位非常赌徒、法国骑士德米尔 (de Mere) 提供的。这个Chevalier de Mere的历史几乎在所有关于概率论的教科书中都有给出。这位骑士在 1654 年的问题在最高科学水平上进行了讨论，在布莱斯·帕斯卡 (Blaise Pascal) 和皮埃尔·费马 (Pierre Fermat) 的通信中进行了讨论。 让我们回顾一下引起这些科学家兴趣的原因是什么，他们的通信在 25 年后的 1679 年发表。他们讨论了在两个略有不同的赌博版本中，赢/输的几率是如何相关的，de Mere 向他的对手提供参与。现在任何熟悉概率论主要原理的学生都会立即帮助骑士解决他的问题，但在三个半世纪前，这个问题只有这样杰出的科学家才能解决。对这个问题的讨论导致了对概率的理解（和定义），即概率是连接实验的有利和不利结果的数量的某种关系，因此，代表玩家兴趣的相应事件可能会出现，也可能不会出现.n相等的（或者，因为以后可能对它们进行限定，等概率的）结果。让我们感兴趣的事件 A 发生，如果任何一个米观察到有利于该事件出现的结果。那么概率磷(一个)事件 A 的发生，由等式给出。 数学代写|概率论代写Probability theory代考|Valery Nevzorov, Mohammad Ahsanullah and Sergei Ananjevskiy 这种获得最大奖金的小概率并没有吓到很多想成为百万富翁的人。结果，大约 400,000 名参与者中就有一人实现了这一目标，并增强了其他人追随他的愿望。所有媒体都立即通知我们有关创纪录的胜利。最近，三个美国人，买了价值2.00每人瓜分强力球彩票中的主要奖金，金额约为 1.5十亿，三个。在这个彩票中，您必须同时猜出 69 个可能的白球中的五个号码和 26 个红球中的一个号码。应对如此复杂组合的机会——大约为 2.92 亿。 有一个有趣的心理时刻。相应彩票的组织者定期发布一组六个最常出现（所有时间或最近）的中奖号码以及一组六个稀有号码。参与者开始猜测，下一轮应该使用哪六个数字中的哪个数字。也许彩票有它的“最爱”，有必要关注前六名吗？其他人反对：“不！后六名的数字将试图超过前六名的同事。我们必须使用它们！” 结果，使用这些列表中的数字的人的比例正在显着增加。由于所有相同的随机数传感器和 Lototron 不会对先前循环的结果做出反应，因此机会均等的新获胜组合可以包含在互联网上标记的这两组数字，以及那些没有进入这两个六的人。在这种情况下应该注意的是，如果一个中奖组合确实包含这 12 个特别分配的数字中的任何一个，那么奖金将分配给在互联网上宣传这些组合的更大的参与者队伍。因此，将这些 Internet 组中未包含的六或五个数字设为有意义的。成功的机会相同，但奖金将分配给少数获胜者。然后奖金将分配给更大的参与者队伍，这些参与者在互联网上发布了这些组合。因此，将这些 Internet 组中未包含的六或五个数字设为有意义的。成功的机会相同，但奖金将分配给少数获胜者。然后奖金将分配给更大的参与者队伍，这些参与者在互联网上发布了这些组合。因此，将这些 Internet 组中未包含的六或五个数字设为有意义的。成功的机会相同，但奖金将分配给少数获胜者。 另一个流行的概率问题与所谓的“快乐”电车、无轨电车或公共汽车票有关。幸运票有两个经典定义。如果前三位数字的总和与后三位数字的总和一致，那么六位数的数字会使票“快乐”。有时在俄罗斯，他们说这代表了幸运彩票的“莫斯科”定义，与之相反的是所谓的“列宁格勒”（或“圣彼得堡”）定义，该定义要求偶数和奇数上的三个数字的总和位置重合。从组合理论的角度来看，这两个定义至少在形式上是不同的，但导致获得幸运票的机会相同。 为完整起见，假设在六位数字（a、b、c、d、e、f）中，六个位置中的任何一个都可以是从零到九的任何数字，即，我们假设存在一张票，其编号为六个零。很明显，可能的票总数正好是一百万。 在评估获得幸运票的机会之前，请考虑以下问题，其解决方案在 N. Ya 的经典著作中有详细描述。维伦金 [NI Vylenkin. 流行组合学，莫斯科：Nauka，1975. 208 页]（另见 [N. Ya. Vylenkin, AN Vilenkin, PA Vilenkin, Combinatorics, M.: FIMA, MCNMO, 2006 – 400 p.]）。 统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。 金融工程代写 金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。 非参数统计代写 非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。 广义线性模型代考 广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。 术语 广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。 有限元方法代写 有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。 有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。 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。 随机分析代写 随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。 时间序列分析代写 随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。 随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。 回归分析代写 多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。 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|概率论代写Probability theory代考|STAT7203 如果你也在 怎样代写概率论Probability theory这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。 概率论是与概率有关的数学分支。虽然有几种不同的概率解释，但概率论以严格的数学方式处理这一概念，通过一套公理来表达它。 statistics-lab™ 为您的留学生涯保驾护航 在代写概率论Probability theory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。我们的专家在代写概率论Probability theory代写方面经验极为丰富，各种代写概率论Probability theory相关的作业也就用不着说。 我们提供的概率论Probability theory及其相关学科的代写，服务范围广, 其中包括但不限于: • 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|概率论代写Probability theory代考|Speed of Convergence in the Strong LLN In the weak law of large numbers, we had a statement on the speed of convergence (Theorem 5.14). In the strong law of large numbers, however, we did not. As we required only first moments, in general, we cannot expect to get any useful statements. However, if we assume the existence of higher moments, we get reasonable estimates on the rate of convergence. The core of the weak law of large numbers is Chebyshev’s inequality. Here we present a stronger inequality that claims the same bound but now for the maximum over all partial sums until a fixed time. Theorem 5.28 (Kolmogorov’s inequality) Let n \in \mathbb{N} and let X_1, X_2, \ldots, X_n be independent random variables with \mathbf{E}\left[X_i\right]=0 and \operatorname{Var}\left[X_i\right]<\infty for i=1, \ldots, n. Further, let S_k=X_1+\ldots+X_k for k=1, \ldots, n. Then, for any t>0,$$
\mathbf{P}\left[\max \left{S_k: k=1, \ldots, n\right} \geq t\right] \leq \frac{\operatorname{Var}\left[S_n\right]}{t^2+\operatorname{Var}\left[S_n\right]}
$$Furthermore, Kolmogorov’s inequality holds:$$
\mathbf{P}\left[\max \left{\left|S_k\right|: k=1, \ldots, n\right] \geq t\right] \leq t^{-2} \operatorname{Var}\left[S_n\right]
$$a generalization of Kolmogorov’s inequality. Proof We decompose the probability space according to the first time \tau at which the partial sums exceed the value t. Hence, let$$
\tau:=\min \left{k \in{1, \ldots, n}: S_k \geq t\right}
$$and A_k={\tau=k} for k=1, \ldots, n. Further, let$$
A=\biguplus_{k=1}^n A_k=\left{\max \left{S_k: k=1, \ldots, n\right} \geq t\right} .
$$Let c \geq 0. The random variable \left(S_k+c\right) \mathbb{1}{A_k} is \sigma\left(X_1, \ldots, X_k\right)-measurable and S_n- S_k is \sigma\left(X{k+1}, \ldots, X_n\right)-measurable. By Theorem 2.26, the two random variables are independent, and$$
\mathbf{E}\left[\left(S_k+c\right) \mathbb{1}{A_k}\left(S_n-S_k\right)\right]=\mathbf{E}\left[\left(S_k+c\right) \mathbb{1}{A_k}\right] \mathbf{E}\left[S_n-S_k\right]=0 .
$$统计代写|概率论代写Probability theory代考|The Poisson Process We develop a model for the number of clicks of a Geiger counter in the (time) interval I=(a, b]. The number of clicks should obey the following rules. It should • be random and independent for disjoint intervals, • be homogeneous in time in the sense that the number of clicks in I=(a, b] has the same distribution as the number of clicks in c+I=(a+c, b+c], • have finite expectation, and • have no double points: At any point of time, the counter makes at most one click. We formalize these requirements by introducing the following notation:$$
\mathcal{I}:={(a, b]: a, b \in[0, \infty), a \leq b},
$$\ell((a, b]):=b-a \quad (the length of the interval I=(a, b]). For I \in \mathcal{I}, let N_I be the number of clicks after time a but no later than b. In particular, we define N_t:=N_{(0, t]} as the total number of clicks until time t. The above requirements translate to: \left(N_I, I \in \mathcal{I}\right) being a family of random variables with values in \mathbb{N}0 and with the following properties: (P1) N{I \cup J}=N_I+N_J if I \cap J=\emptyset and I \cup J \in \mathcal{I}. (P2) The distribution of N_I depends only on the length of I: \mathbf{P}{N_I}=\mathbf{P}{N_J} for all I, J \in \mathcal{I} with \ell(I)=\ell(J). (P3) If \mathcal{J} \subset \mathcal{I} with I \cap J=\emptyset for all I, J \in \mathcal{J} with I \neq J, then \left(N_J, J \in \mathcal{J}\right) is an independent family. (P4) For any I \in \mathcal{I}, we have \mathbf{E}\left[N_I\right]<\infty. (P5) \lim \sup {\varepsilon \downarrow 0} \varepsilon^{-1} \mathbf{P}\left[N{\varepsilon} \geq 2\right]=0. The meaning of (P5) is explained by the following calculation. Define$$
\lambda:=\underset{\varepsilon \downarrow 0}{\lim \sup } \varepsilon^{-1} \mathbf{P}\left[N_{\varepsilon} \geq 2\right] .
$$概率论代考 统计代写|概率论代写概率论代考|强LLN的收敛速度 在弱大数定律中，我们有一个关于收敛速度的陈述(定理5.14)。然而，在强大数定律中，我们没有。由于我们只要求第一时刻，一般来说，我们不能期望得到任何有用的说明。但是，如果我们假设存在更高的矩，我们就可以得到关于收敛速度的合理估计 弱大数定律的核心是切比雪夫不等式。在这里，我们提出了一个更强的不等式，它要求相同的边界，但现在是在固定时间之前的所有部分和上的最大值 定理5.28 (Kolmogorov’s不等式)设n \in \mathbb{N}和X_1, X_2, \ldots, X_n为独立随机变量，\mathbf{E}\left[X_i\right]=0和\operatorname{Var}\left[X_i\right]<\infty为i=1, \ldots, n。进一步，设S_k=X_1+\ldots+X_k for k=1, \ldots, n。然后，对于任何t>0，$$
\mathbf{P}\left[\max \left{S_k: k=1, \ldots, n\right} \geq t\right] \leq \frac{\operatorname{Var}\left[S_n\right]}{t^2+\operatorname{Var}\left[S_n\right]}
$$进一步，Kolmogorov不等式成立:$$
\mathbf{P}\left[\max \left{\left|S_k\right|: k=1, \ldots, n\right] \geq t\right] \leq t^{-2} \operatorname{Var}\left[S_n\right]
$$Kolmogorov不等式的推广 我们根据第一次\tau的部分和超过t的值来分解概率空间。因此，让$$
\tau:=\min \left{k \in{1, \ldots, n}: S_k \geq t\right}
$$和A_k={\tau=k} for k=1, \ldots, n。进一步，让$$
A=\biguplus_{k=1}^n A_k=\left{\max \left{S_k: k=1, \ldots, n\right} \geq t\right} .
$$让c \geq 0。随机变量\left(S_k+c\right) \mathbb{1}{A_k}是\sigma\left(X_1, \ldots, X_k\right) -可测量，S_n-$$S_k$是$\sigma\left(X{k+1}, \ldots, X_n\right)$-可测量。根据定理$2.26$，两个随机变量是独立的， $$\mathbf{E}\left[\left(S_k+c\right) \mathbb{1}{A_k}\left(S_n-S_k\right)\right]=\mathbf{E}\left[\left(S_k+c\right) \mathbb{1}{A_k}\right] \mathbf{E}\left[S_n-S_k\right]=0 .$$ 统计代写|概率论代写概率论代考|泊松过程 我们为盖革计数器在(时间)间隔$I=(a, b]$内的点击数开发了一个模型。点击次数应遵循以下规则。它应该 • 对于不连续区间是随机独立的， • 在时间上是均匀的，就点击的数量而言$I=(a, b]$是否与点击数的分布相同$c+I=(a+c, b+c]$， • 有有限的期望， • 没有双点:在任何时间点，计数器最多做一次点击。我们通过引入以下符号来形式化这些要求$$\mathcal{I}:={(a, b]: a, b \in[0, \infty), a \leq b},$$$\ell((a, b]):=b-a \quad$(间隔的长度$I=(a, b])$. 用于$I \in \mathcal{I}$，让$N_I$是点击次数之后的时间$a$但不迟于$b$。特别地，我们定义$N_t:=N_{(0, t]}$作为总点击数，直到时间$t$。上述要求可译为:$\left(N_I, I \in \mathcal{I}\right)$是一组随机变量的值$\mathbb{N}0$并具有以下性质:(P1)$N{I \cup J}=N_I+N_J$如果$I \cap J=\emptyset$和$I \cup J \in \mathcal{I}$. (P2)的分布$N_I$只取决于的长度$I: \mathbf{P}{N_I}=\mathbf{P}{N_J}$为所有人$I, J \in \mathcal{I}$用$\ell(I)=\ell(J)$. (P3)如果$\mathcal{J} \subset \mathcal{I}$用$I \cap J=\emptyset$为所有人$I, J \in \mathcal{J}$用$I \neq J$，那么$\left(N_J, J \in \mathcal{J}\right)$(P4)对于任何$I \in \mathcal{I}$，我们有$\mathbf{E}\left[N_I\right]<\infty$. (P5)$\lim \sup {\varepsilon \downarrow 0} \varepsilon^{-1} \mathbf{P}\left[N{\varepsilon} \geq 2\right]=0\$.
(P5)的含义通过以下计算来解释。定义
$$\lambda:=\underset{\varepsilon \downarrow 0}{\lim \sup } \varepsilon^{-1} \mathbf{P}\left[N_{\varepsilon} \geq 2\right] .$$

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。