电子工程代写|计算数学基础代写Mathematical Foundations of Computing代考|CS5850

statistics-lab™ 为您的留学生涯保驾护航 在代写计算数学基础Mathematical Foundations of Computing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。我们的专家在代写计算数学基础Mathematical Foundations of Computing方面经验极为丰富，各种代写计算数学基础Mathematical Foundations of Computing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

电子工程代写|计算数学基础代写Mathematical Foundations of Computing代考|Random Variables

So far, we have restricted ourselves to studying events, which are collections of outcomes of experiments or observations. However, we are often interested in abstract quantities or outcomes of experiments that are derived from events and observations but are not themselves events or observations. For example, if we throw a fair die, we may want to compute the probability that the square of the face value is smaller than 10. This is random and can be associated with a probability and, moreover, depends on some underlying random events. Yet, it is neither an event nor an observation: It is a random variable. Intuitively, a random variable is a quantity that can assume any one of a set of values, called its domain $\boldsymbol{D}$, and whose value can be stated only probabilistically. In this section, we will study random variables and their distributions.

More formally, a real random variable-the one most commonly encountered in applications having to do with computer networking-is a mapping from events in a sample space $S$ to the domain of real numbers. The probability associated with each value assumed by a real random variable ${ }^{2}$ is the probability of the underlying event in the sample space, as illustrated in Figure 1.1.

A random variable is discrete if the set of values it can assume is finite and countable. The elements of $D$ should be mutually exclusive-that is, the random variable cannot simultaneously take on more than one value-and exhaustive-the random variable cannot assume a value that is not an element of $D$.

电子工程代写|计算数学基础代写Mathematical Foundations of Computing代考|Cumulative Density Function

The domain of a discrete real random variable $X_{d}$ is totally ordered; that is, for any two values $x_{1}$ and $x_{2}$ in the domain, either $x_{1}>x_{2}$ or $x_{2}>x_{1}$. We define the cumulative density function $F\left(X_{d}\right)$ by
$$F(x)=\sum_{i \mid x_{i} \leq x} p\left(x_{i}\right)=p\left(X_{d} \leq x\right)$$
Note the difference between $F\left(X_{d}\right)$, which denotes the cumulative distribution of random variable $X_{d}$, and $F(x)$, which is the value of the cumulative distribution for the value $X_{d}=x$

Similarly, the cumulative density function of a continuous random variable $X_{c}$, denoted $F\left(X_{c}\right)$, is given by
$$F(x)=\int_{-\infty}^{x} f(y) d y=p\left(X_{c} \leq x\right)$$
By definition of probability, in both cases, $0 \leq F\left(X_{d}\right) \leq 1,0 \leq F\left(X_{c}\right) \leq 1$.

电子工程代写|计算数学基础代写Mathematical Foundations of Computing代考|Cumulative Density Function

$$F(x)=\sum_{i \mid x_{i} \leq x} p\left(x_{i}\right)=p\left(X_{d} \leq x\right)$$

$$F(x)=\int_{-\infty}^{x} f(y) d y=p\left(X_{c} \leq x\right)$$

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。