assignmentutor-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
• 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

## 数学代写|概率论代写Probability theory代考|DEFINITIONS AND EXAMPLES

Up to these times we basically dealt with random objects representing independent random variables. For example, for working with the sequence of independent variables $\xi_{1}, \xi_{2}, \ldots$ it is often enough to know the set of the distribution functions or the corresponding characteristic functions. Our reader remembers that in this case work with sums of independent summands is not essentially complicated: it is enough to remember that this sum corresponds to a product of characteristic functions, and if a product of such independent variables is given, then we can remember that the expected value of such a product is expressed simply in terms of products of individual mean values (if they exist) of the random factors. It becomes essentially more unpleasant to deal with dependent random variables, even if this dependence is not so complicated. In this case, for example, already for finding the dispersion of a sum of several dependent summands not only variances of the individual summands should be known but also all the mixed moments as covariances of these random variables. So, prima facie the situation becomes rather wonderful when dealing with a set of independent variables we consciously go to regarding some random variable transformations leading to wittingly dependent random objects. Order statistics are an example of such objects.
1) Let there be a batch of some details (for example, incandescent light bulbs), that must satisfy some standards (for example, the mean time of work should be not less than some value $t$ ). The question is dealt about dealing this batch from a seller to a customer. How can the seller persuade the customer in the compliance of the production to the standard? The simplest thing is to display all the details to the test bench, to get all the data amount their longevity, to count the average longevity and to say that this concrete batch that became broken satisfied all the necessary quantities and qualities.

## 数学代写|概率论代写Probability theory代考|DISTRIBUTIONS OF ORDER STATISTICS

Let there be $n$ random variables in a probability space $X_{1}, X_{2}, \ldots, X_{n}$ and this set corresponds to the variational series $X_{l, n} \leq X_{2, n} \leq \ldots \leq X_{n, n}$.

We suppose that the original random variables are independent and have a common cumulative distribution function $F(x)$. In this case cumulative distribution functions of the extreme members of the variational series (order statistics $X_{l, n}$ and $X_{n, n}$ ) seem very simple. It is easy to verify, taking independence of the initial variables into account, that
$$\mathrm{F}{\mathrm{n}, \mathrm{n}}(\mathrm{x})=\mathrm{P}\left{\mathrm{X}{\mathrm{n}, \mathrm{n}}<\mathrm{x}\right}=\mathrm{P}\left{\mathrm{X}{1}<\mathrm{x}, \mathrm{X}{2}<\mathrm{x}, \ldots, \mathrm{X}{\mathrm{n}}<\mathrm{x}\right}=\mathrm{F}^{\mathrm{n}}(\mathrm{x})$$ and \begin{aligned} &F{1, n}(x)=P\left{X_{1, n}<x\right}=1-P\left{X_{1, n} \geq x\right} \ &=1-P\left{X_{1} \geq x, X_{2} \geq x, \ldots, X_{n} \geq x\right}=1-(1-F(x))^{n} \end{aligned}
Already for the order statistic $X_{n-1, n}$ it would be needed to use a more cumbersome relation
\begin{aligned} &\mathrm{F}{\mathrm{n}-1, \mathrm{n}}(\mathrm{x})=\mathrm{P}\left{\mathrm{X}{\mathrm{n}-1, \mathrm{n}}<\mathrm{x}\right}=\mathrm{P}\left{\mathrm{X}{\mathrm{n}, \mathrm{n}}<\mathrm{x}\right}+\mathrm{P}\left{\mathrm{X}{\mathrm{n}-1, \mathrm{n}}<\mathrm{x}, \mathrm{X}_{\mathrm{n}, \mathrm{n}} \geq \mathrm{x}\right}= \ &=\mathrm{F}^{\mathrm{n}}(\mathrm{x})+\mathrm{n}(1-\mathrm{F}(\mathrm{x})) \mathrm{F}^{\mathrm{n}-1}(\mathrm{x}) . \end{aligned}

# 概率论代考

## 数学代写|概率论代写Probability theory代考|DEFINITIONS AND EXAMPLES

1）假设有一批一些细节（例如白炽灯泡），必须满足一些标准（例如，平均工作时间应该不小于某个值吨）。问题是关于将这批从卖方到客户的交易。卖方如何说服客户生产符合标准？最简单的事情是在测试台上显示所有细节，获取所有数据来衡量它们的寿命，计算平均寿命，然后说这批破碎的混凝土满足了所有必要的数量和质量。

## 数学代写|概率论代写Probability theory代考|DISTRIBUTIONS OF ORDER STATISTICS

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## 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。

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