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assignmentutor-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代写方面经验极为丰富，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|统计推断代写Statistical inference代考|The Notion of a Random Variable: A Naive View

The notion of a random variable constitutes one of the most important concepts in the theory of probability. For a proper understanding of the concept, the reader is required to read through to Chapter 3 . In order to come to grips with the notion at an intuitive level, however, let us consider the naive view first introduced by Chebyshev (1821-1884) in the middle of the nineteenth century, who defined a random variable as:
a real variable that assumes different values with different probabilities.
This definition comes close to the spirit of the modern concept, but it leaves a lot to be desired from the mathematical viewpoint.

As shown in Chapter 3, a random variable is a function from a set of outcomes to the real line; attaching numbers to outcomes! The need to define such a function arises because the outcomes of certain stochastic phenomena do not always come in the form of numbers but the data often do. The naive view of a random variable suppresses the set of outcomes and identifies the notion of a random variable with its range of values $\mathbb{R}_{X}$; hence the term variable.

Example 2.3 In the case of the experiment of casting two dice and looking at the uppermost faces, discussed in Chapter 1, the outcomes come in the form of combinations of die faces (not numbers!), all 36 such combinations, denoted by, say, $\left{s_{1}, s_{2}, \ldots, s_{36}\right}$. Let us assume that we are interested in the sum of dots appearing on the two faces. This amounts to defining a random variable
$$X(.):\left{s_{1}, s_{2}, \ldots, s_{36}\right} \rightarrow \mathbb{R}{X}:={2,3, \ldots, 12} .$$ However, this is not the only random variable we could have defined. Another one might be $$Y(.):\left{s{1}, s_{2}, \ldots, s_{36}\right} \rightarrow{0,1},$$
if we want to define the outcomes even $(Y=0)$ and odd $(Y=1)$. This example suggests that ignoring the outcomes set and identifying the random variable with its range of values can be misleading. Be that as it may, let us take this interpretation at face value and proceed to consider the other important dimension of the naive view of a random variable: its randomness. The simplest way to explain this dimension is to return to the above example.

## 统计代写|统计推断代写Statistical inference代考|Continuous Random Variables

The above example involves two random variables which comply perfectly with Chebyshev’s naive definition. With each value of the random variable we associate a probability. This is because both random variables are discrete: their range of values is countable. On the other hand, when a random variable takes values over an interval, i.e. its range of values is uncountable, things are not as simple. Attaching probabilities to particular values does not work (see Chapter 3), and instead we associate probabilities with small intervals which belong to this range of values. Instead of (2.6), the density function for continuous random variables is defined over intervals as follows:
$$\mathbb{P}(x \leq X<x+d x)=f(x) d x, \text { for all } x \in \mathbb{R}{X},$$ and satisfies the properties (a) $f{x}(x) \geq 0$, for all $x \in \mathbb{R}{X}$; (b) $\int{x \in \mathbb{R}{X}} f{x}(x) d x=1$
It is important to note that the density function for continuous random variables takes values in the interval $[0, \infty)$; its values cannot be interpreted as probabilities. In contrast, the density function for discrete random variables takes values in the interval $[0,1]$.

# 统计推断代考

## 统计代写|统计推断代写Statistical inference代考|The Notion of a Random Variable: A Naive View

：假设具有不同概率的不同值。

\left 的分隔符缺失或无法识别\left 的分隔符缺失或无法识别然而，这不是我们可以定义的唯一随机变量。另一个可能是\left 的分隔符缺失或无法识别\left 的分隔符缺失或无法识别

## 统计代写|统计推断代写Statistical inference代考|Continuous Random Variables

$$\mathbb{P}(x \leq X<x+d x)=f(x) d x, \text { for all } x \in \mathbb{R} X$$

## 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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师