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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 Case of an Uncountable Outcomes Set S

As a prelude to the discussion that follows, let us see why the previous strategy of assigning probabilities to each and every outcome in the case of an uncountable set, say $S=\mathbb{R}$, will not work. The reason is very simple: the outcomes set has so many elements that it is impossible to arrange them in a sequence and thus count them. Hence, any attempt to follow the procedure used in the countable outcomes set case will lead to insurmountable difficulties. Intuitively, we know that we cannot cover the real line point by point. The only way to overlay $\mathbb{R}$ or any of its uncountable subsets is to use a sequence of intervals of any one of the following forms:
$(a, b),[a, b],[a, b),(-\infty, a]$, where $a<b, a$ and $b$ real numbers.
We will see in the sequel that the most convenient form for such intervals is ${(-\infty, x]}$ for each $x \in \mathbb{R}$.

In view of the above discussion, any attempt to define a random variable using the definition of a discrete random variable
$X(.): S \rightarrow \mathbb{R}_X$, such that ${s: X(s)=x}:=X^{-1}(x) \in \mathfrak{I}$ for all $x \in \mathbb{R}$
is doomed to failure. We have just agreed that the only way we can overlay $\mathbb{R}$ is by using intervals not points. The half-infinite intervals (3.10) suggest the modification of the events ${s: X(s)=x}$ of (3.11) into events of the form ${s: X(s) \leq x}$.

A random variable relative to $\Im$ is a function $X(.): S \rightarrow \mathbb{R}$ that satisfies the restriction
$${s: X(s) \leq x}:=X^{-1}((-\infty, x]) \in \mathfrak{I} \text { for all } x \in \mathbb{R} \text {. }$$
Notice that the only difference between this definition and that of a discrete random variable comes in the form of the events used.
$${s: X(s)=x} \subset{s: X(s) \leq x},$$
Moreover, in view of the fact that the latter definition includes the former as a special case. From this definition we can see that the pre-image of the random variable $X(.)$ takes us from intervals $(-\infty, x], x \in \mathbb{R}$ back to the event space $\Im$. The set of all such intervals generates a $\sigma$-field on the real line known as the Borel field and denoted by $\mathcal{B}(\mathbb{R})$ :
$$\mathcal{B}(\mathbb{R})=\sigma((-\infty, x], x \in \mathbb{R})$$

## 统计代写|统计推断代写Statistical inference代考|The Concept of a Cumulative Distribution Function

Using the concept of a random variable $X(.)$, so far we have transformed the abstract probability space $(S, \Im, \mathbb{P}(.))$ into a less abstract space $\left(\mathbb{R}, \mathcal{B}(\mathbb{R}), P_X(.)\right)$. However, we have not reached our target yet, because $P_X(.):=\mathbb{P} X^{-1}(.)$ is still a set function. Admittedly it is a much easier set function, because it is defined on the real line, but a set function all the same. What we prefer is a numerical point-to-point function.

The way we transform the set function $P_X$ (.) into a numerical point-to-point function is by a clever stratagem. By viewing $P_X(.)$ as only a function of the end point of the interval $(-\infty, x]$, we define the cumulative distribution function (cdf)
$$F_X(.): \mathbb{R} \rightarrow[0,1], \text { defined by } F_X(x)=\mathbb{P}{s: X(s) \leq x}=P_X((-\infty, x]) .$$

The ploy leading to this trick began a few pages ago when we argued that even though we could use any one of the following intervals (see Galambos, 1995):
$(a, b),[a, b],[a, b),(-\infty, a]$, where $a<b, a \in \mathbb{R}$, and $b \in \mathbb{R}$
to generate the Borel field $\mathcal{B}(\mathbb{R})$, we chose intervals of the form $(-\infty, x], x \in \mathbb{R}$.
In view of this, we can think of the cdf as being defined via
$$\mathbb{P}{s: a<X(s) \leq b}=\mathbb{P}{s: X(s) \leq b}-\mathbb{P}{s: X(s) \leq a}=P_X((a, b])=F_X(b)-F_X(a),$$
and then assume that $F_X(-\infty)=0$.
The properties of the $\operatorname{cdf} F_X(x)$ in Table $3.3$, where $x \rightarrow x_0^{+}$reads “as $x$ tends to $x_0$ through values greater than $x_0$,” are determined by those of $(S, \Im, \mathbb{P}(.))$. In particular from axioms [A1]-[A3] of $\mathbb{P}(.)$ and the mathematical structure of the $\sigma$-fields $\Im$ and $\mathcal{B}(\mathbb{R})$; see Karr (1993). That is, $F_X(x)$ is a non-decreasing, right-continuous function such that $F_X(-\infty)=0$, and $F_X(\infty)=1$. Properties $\mathrm{F} 1$ and $\mathrm{F} 3$ need no further explanation, but $\mathrm{F} 2$ is not obvious. The right-continuity property of the cdf follows from the axiom of countable additivity [3] of the probability set function $\mathbb{P}(.)$, whose value stems from the fact that at every point of discontinuity $x_0, \mathrm{~F} 2$ holds.

# 统计推断代考

## 统计代写|统计推断代写统计推断代考|不可数结果集S的情况

$(a, b),[a, b],[a, b),(-\infty, a]$，其中$a<b, a$和$b$实数。我们将在续集中看到，这种间隔最方便的形式是${(-\infty, x]}$对应每个$x \in \mathbb{R}$ .

$X(.): S \rightarrow \mathbb{R}_X$定义随机变量的尝试，使${s: X(s)=x}:=X^{-1}(x) \in \mathfrak{I}$对于所有$x \in \mathbb{R}$

$${s: X(s) \leq x}:=X^{-1}((-\infty, x]) \in \mathfrak{I} \text { for all } x \in \mathbb{R} \text {. }$$

$${s: X(s)=x} \subset{s: X(s) \leq x},$$

$$\mathcal{B}(\mathbb{R})=\sigma((-\infty, x], x \in \mathbb{R})$$ 表示

## 统计代写|统计推断代写统计推断代考|累积分布函数的概念

$$F_X(.): \mathbb{R} \rightarrow[0,1], \text { defined by } F_X(x)=\mathbb{P}{s: X(s) \leq x}=P_X((-\infty, x]) .$$

$(a, b),[a, b],[a, b),(-\infty, a]$，其中$a<b, a \in \mathbb{R}$，和$b \in \mathbb{R}$

$$\mathbb{P}{s: a<X(s) \leq b}=\mathbb{P}{s: X(s) \leq b}-\mathbb{P}{s: X(s) \leq a}=P_X((a, b])=F_X(b)-F_X(a),$$
，然后假设$F_X(-\infty)=0$ .

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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