# 电气工程代写|模拟和数字通信代写Analogue and Digital Communications代考|EE179 Cumulative Distribution Function

my-assignmentexpert™提供最专业的一站式服务：Essay代写，Dissertation代写，Assignment代写，Paper代写，Proposal代写，Proposal代写，Literature Review代写，Online Course，Exam代考等等。my-assignmentexpert™专注为留学生提供Essay代写服务，拥有各个专业的博硕教师团队帮您代写，免费修改及辅导，保证成果完成的效率和质量。同时有多家检测平台帐号，包括Turnitin高级账户，检测论文不会留痕，写好后检测修改，放心可靠，经得起任何考验！

## 电气工程代写|模拟和数字通信代写Analogue and Digital Communications代考|Cumulative Distribution Function

The cumulative distribution function (CDF) is defined as
$$F_X(x)=\int_{-\infty}^x f_X(\sigma) d \sigma$$
it is the probability
$$P(-\infty<X<x)=F_X(x)$$
therefore the probability that $x_1 \leq X \leq x_2$ is
$$F_X\left(x_2\right)-F_X\left(x_1\right)$$
the CDF has the following two important properties

1. $F_X(x)$ is bounded by zero and one.
$$0 \leq F_X(x) \leq 1$$
which is proved using Eq. (3.28).
2. The CDF is monotonically increasing
$$F_X\left(x_2\right)>F_X\left(x_1\right) \quad \text { when } x_2>x_1$$

## 电气工程代写|模拟和数字通信代写Analogue and Digital Communications代考|Examples of Random Variables

Discrete random variable occurs when the random variable only takes on discrete values, as the following example suggests.

Example 3.10 Find the probability density function and cumulative distribution function of the random variable corresponding to the toss of a dice.

The toss of a dice is a discrete random variable. From the discussion given, the PDF generally applies to a continuous random variable. However we may use a discrete approach to the problem. The discrete approach implies that we use summation rather than integration, and the notation is the $f_X[x]$ where the square brackets implies a discrete random variable. Then
$$f_X[x]= \begin{cases}\frac{1}{6} & \text { for } 1 \leq x \leq 6, x=1, \ldots 6 \ 0 & 0 \text { elsewhere }\end{cases}$$
using this notation
$$F_X[x]=\sum_{n=1}^x f_X[x]=\frac{x}{6} \text { where } x=1, \ldots 6$$
The problem which we can envisage is that in the most general case some particular random variable may take continuous values in some intervals and discrete values at some points. So to make Eqs. (3.33) and (3.34), ‘continuous’ we use the property of a unit impulse:
$$\int_{-\infty}^{\infty} \delta(\sigma) d \sigma=1$$
which gives us
$$f_X(x)= \begin{cases}\sum_{x_0=1}^6 \frac{1}{6} \delta\left(x-x_0\right) & \text { for } 1 \leq x_0 \leq 6, x_0=1, \ldots 6 \ 0 & 0 \text { elsewhere }\end{cases}$$
and
$$F_X(x)=\int_{\sigma=-\infty}^x f_X(\sigma) d \sigma$$
the PDF and CDF of this random variable are shown in Fig. 3.7.

## 电气工程代写|模拟和数字通信代写ANALOGUE AND DIGITAL COMMUNICATIONS代考|CUMULATIVE DISTRIBUTION FUNCTION

$$F_X(x)=\int_{-\infty}^x f_X(\sigma) d \sigma$$

$$P(-\infty<X<x)=F_X(x)$$

$$F_X\left(x_2\right)-F_X\left(x_1\right)$$
CDF具有以下两个重要属性

$F_X(x)$ 以雺和一为界。
$$0 \leq F_X(x) \leq 1$$

CDF 单调曽增
$$F_X\left(x_2\right)>F_X\left(x_1\right) \quad \text { when } x_2>x_1$$

## 电气工程代写|模拟和数字通信代写ANALOGUE AND DIGITAL COMMUNICATIONS代考|EXAMPLES OF RANDOM VARIABLES

$$f_X[x]=\left{\frac{1}{0} \quad \text { for } 1 \leq x \leq 6, x=1, \ldots 60 \quad 0\right. \text { elsewhere }$$

$$F_X[x]=\sum_{n=1}^x f_X[x]=\frac{x}{6} \text { where } x=1, \ldots 6$$

$$\int_{-\infty}^{\infty} \delta(\sigma) d \sigma=1$$

$$f_X(x)=\left{\sum_{x_0=1}^6 \frac{1}{6} \delta\left(x-x_0\right) \quad \text { for } 1 \leq x_0 \leq 6, x_0=1, \ldots 60 \quad 0\right. \text { elsewhere }$$

$$F_X(x)=\int_{\sigma=-\infty}^x f_X(\sigma) d \sigma$$

## 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。