### 统计代写|统计推断作业代写statistical inference代考|Facts about expected values

statistics-lab™ 为您的留学生涯保驾护航 在代写 统计推断statistical inference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。我们的专家在代写统计推断statistical inference方面经验极为丰富，各种代写 统计推断statistical inference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

## 统计代写|统计推断作业代写statistical inference代考|Facts about expected values

Recall that expected values are properties of population distributions. The expected value, or mean, height is the center of the population density of heights.
Of course, the average of ten randomly sampled people’s height is itself of random variable, in the same way that the average of ten die rolls is itself a random number. Thus, the distribution of heights gives rise to the distribution of averages of ten heights in the same way that distribution associated with a die roll gives rise to the distribution of the average of ten dice.

An important question to ask is: “What does the distribution of averages look like?”. This question is important, since it tells us things about averages, the best way to estimate the population mean, when we only get to observe one average.

Consider the die rolls again. If wanted to know the distribution of averages of 100 die rolls, you could (at least in principle) roll 100 dice, take the average and repeat that process. Imagine, if you could only roll the 100 dice once. Then we would have direct information about the distribution of die rolls (since we have 100 of them), but we wouldn’t have any direct information about the distribution of the average of 100 die rolls, since we only observed one average.

Fortunately, the mathematics tells us about that distribution. Notably, it’s centered at the same spot as the original distribution! Thus, the distribution of the estimator (the sample mean) is centered at the distribution of what it’s estimating (the population mean). When the expected value of an estimator is what its trying to estimate, we say that the estimator is unbiased.
Let’s go through several simulation experiments to see this more fully.

## 统计代写|统计推断作业代写statistical inference代考|Exercises

A standard die takes the values $1,2,3,4,5,6$ with equal probability. What is the expected value?

1. Consider a density that is uniform from -1 to 1. (I.e. has height equal to $1 / 2$ and looks like a box starting at $-1$ and ending at 1 ). What is the mean of this distribution?
If a population has mean $\mu$, what is the mean of the distribution of averages of 20 observations from this distribution?

You are playing a game with a friend where you flip a coin and if it comes up heads you give her $X$ dollars and if it comes up tails she gives you $\$ Y \ dollars. The odds that the coin is heads is $d$. What is your expected earnings? Watch a video of the solution to this problem and look at the problem and the solution here..
If you roll ten standard dice, take their average, then repeat this process over and over and construct a histogram what would it be centered at? Watch a video solution here and see the original problem here.

## 统计代写|统计推断作业代写statistical inference代考|The variance

Recall that the mean of distribution was a measure of its center. The variance, on the other hand, is a measure of spread. To get a sense, the plot below shows a series of increasing variances.

We saw another example of how variances changed in the last chapter when we looked at the distribution of averages; they were always centered at the same spot as the original distribution, but are less spread out. Thus, it is less likely for sample means to be far away from the population mean than it is for individual observations. (This is why the sample mean is a better estimate than the population mean.)

If $X$ is a random variable with mean $\mu$, the variance of $X$ is defined as $\operatorname{Var}(X)=E\left[(X-\mu)^{2}\right]=E\left[X^{2}\right]-E[X]^{2}$
The rightmost equation is the shortcut formula that is almost always used for calculating variances in practice.
Thus the variance is the expected (squared) distance from the mean. Densities with a higher variance are more spread out than densities with a lower variance. The square root of the variance is called the standard deviation. The main benefit of working with standard deviations is that they have the same units as the data, whereas the variance has the units squared.
In this class, we’ll only cover a few basic examples for calculating a variance. Otherwise, we’re going to use the ideas without the formalism. Also remember, what we’re talking about is the population variance. It measures how spread out the population of interest is, unlike the sample variance which measures how spread out the observed data are. Just like the sample mean estimates the population mean, the sample variance will estimate the population variance.

## 统计代写|统计推断作业代写statistical inference代考|Exercises

1. 考虑一个从 -1 到 1 的均匀密度。（即高度等于1/2看起来像一个盒子−1并以 1 结束）。这种分布的平均值是什么？
如果人口有均值μ，这个分布的 20 个观测值的平均值分布的平均值是多少？

## 广义线性模型代考

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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。