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

## 数学代写|概率论代写Probability theory代考|STABLE DISTRIBUTION

A random variable $\mathrm{X}$ is defined as stable distribution if for any two independent copies $\mathrm{X}1, \mathrm{X}_2$ and for any two positive numbers $\mathrm{a}$ and $\mathrm{b}$, there exist a positive number $\mathrm{c}$ and a real number $\mathrm{d}$ such that $\mathrm{a} \mathrm{X}_1+\mathrm{bX} \mathrm{X}_2$ and $\mathrm{c} \mathrm{X}+\mathrm{d}$ are identically distributed. If $\mathrm{d}=0$, then we say $\mathrm{X}$ is strictly stable. .An alternative definition of stable random variable is as follows. Suppose $X_1$, $X_2, \ldots, X_n$ are independent copies of $X$, then for $\mathrm{n} \geq 2, \mathrm{~W}=X_1+X_2+\ldots . .+X_n$ and $\mathrm{c}{\mathrm{n}} \mathrm{X}+\mathrm{d}$ are identically distributed. The normal, Cauchy and Levy distributions have closed form stable distribution.
If $\mathrm{X}$ is standard normal, then $\frac{X x_1+X_2+\cdots+X_n}{\sqrt{n}}$ is standard normal. If $\mathrm{X}$ is standard Cauchy, then $\frac{X_1+X_2+\cdots+X_n}{n}$ is standard Cauchy. If $\mathrm{X}$ is standard Levy, then $\frac{X_1+X_2+\cdots+X_n}{n^2}$ is standard Levy. If $\mathrm{X}$ has standard normal, then $c_n=\sqrt{n}$ and $d=0$.
If $\mathrm{X}$ has standard Cauchy distribution, then $\mathrm{c}{\mathrm{n}}=\mathrm{n}$ and $\mathrm{d}=0$ If $\mathrm{X}$ has $\mathrm{r}$ standard Levy distribution, then $c_n=n^2$ and $\mathrm{d}{\mathrm{n}}=0$.

## 数学代写|概率论代写Probability theory代考|STUDENT T-DISTRIBUTION

A random variable $\mathrm{X}$ has the Student-t distribution if the pdf is as follows.
$$\mathrm{f}(\mathrm{x})=\frac{1}{\sqrt{\pi} B\left(\frac{m}{2} \cdot \frac{1}{2}\right)}\left(\left(1+\frac{t^2}{n}\right)^{-(n+1) / 2},-\infty0 .\right.$$
$\mathrm{n}$ is known as degrees of freedom, We denote the Student-t distribution with $\mathrm{n}$ degrees of freedom as ST(n).
The pdfs of, ST(1), ST(3) and ST(24) are given in Figure 4.17.

Mean $\quad 0$ if $\mathrm{n}>1$, undefined for $\mathrm{n}=1$
Variance $\frac{n}{n-2}, n>2$
Moment about the origin $\mathrm{E}\left(\mathrm{X}^{\mathrm{k}}\right)=0$ if $\mathrm{k}$ is odd
$$=\prod_{i=0}^{k / 2} \frac{2 i-1}{n=2 i}$$
Moment generating function does not exist.
Characteristic function $\quad \psi_n(t)-\frac{1}{\pi \Gamma(n / 2)}\left(\frac{|t|}{2 \sqrt{n}}\right)^{n / 2} Y_{n / 2}\left(\frac{|t|}{\sqrt{n}}\right)$
where $\mathrm{Y}_{\mathrm{n} / 2}($.$) is the Bessel function of the second kind$

# 概率论代考

## 数学代写|概率论代写Probability theory代考|STUDENT T-DISTRIBUTION

$$\mathrm{f}(\mathrm{x})=\frac{1}{\sqrt{\pi} B\left(\frac{m}{2} \cdot \frac{1}{2}\right)}\left(\left(1+\frac{t^2}{n}\right)^{-(n+1) / 2},-\infty 0 .\right.$$
$\mathrm{n}$ 被称为自由度，我们将 Student-t 分布表示为 $n$ 自由度为 $\mathrm{ST}(\mathrm{n})$ 。

$$=\prod_{i=0}^{k / 2} \frac{2 i-1}{n=2 i}$$

myassignments-help数学代考价格说明

1、客户需提供物理代考的网址，相关账户，以及课程名称，Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明，让您清楚的知道您的钱花在什么地方。

2、数学代写一般每篇报价约为600—1000rmb，费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵)，报价后价格觉得合适，可以先付一周的款，我们帮你试做，满意后再继续，遇到Fail全额退款。

3、myassignments-help公司所有MATH作业代写服务支持付半款，全款，周付款，周付款一方面方便大家查阅自己的分数，一方面也方便大家资金周转，注意:每周固定周一时先预付下周的定金，不付定金不予继续做。物理代写一次性付清打9.5折。

Math作业代写、数学代写常见问题

myassignments-help擅长领域包含但不是全部: