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电气工程代写|模拟和数字通信代写Analogue and Digital Communications代考|ECE4664 Conditional Probability and Independent Events

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电气工程代写|模拟和数字通信代写Analogue and Digital Communications代考|Conditional Probability and Independent Events

Suppose we have a sample space, $\mathcal{S}$, which contains two events, $A$ and $B$. The probability of occurrence of the event $A$ is $P(A)$, and that of $B$ is $P(B)$. We want to find the probability of occurrence of the joint event $A \cap B$, which is the same as saying, “the probability of occurrence of events $A$ and $B$ taking place …” Let us look at the following experiment: two dice are tossed, a green one and a blue one. Two people are involved, you and another person. The other person can see result of the result of the fall of the dice, but you cannot. The event $A$ is: a ‘1’ appears on the green die, while the event $B$ is a ‘ 2 ‘ appears on the blue die. The two sample spaces are $(($ green outcome, blue outcome $))$
\begin{aligned} &A={(1,1) \ldots(1,6)} \quad \text { (6 outcomes) } \ &B={(1,2),(2,2), \ldots(6,2)} \quad \text { (6 outcomes) } \end{aligned}
and
\begin{aligned} A \cap B &={(1,2)} \ P(A \cap B) &=\frac{1}{36} \end{aligned}
where the event $A \cap B$ is ‘ 1 ‘ appears on the green die and ‘ 2 ‘ appears on the blue die. Now the two dice are tossed. There will be many outcomes when neither a ‘ 1 ‘ or ‘ 2 ‘ appear. However, when a ‘ 2 ‘ appears on the blue die the other person announces it: “a ‘ 2 ‘ has appeared on the blue die”. Now the probability of occurrence of ‘ 1 ‘ appearing on the green die has increased to $1 / 6$ : the probability of occurrence of the conditional event $P(A \mid B)=1 / 6$, (read as “probability of occurrence of the event $A$ given $B$ has occurred) since the sample space
$$A \mid B={(1,2),(2,2) \ldots(6,2)} \quad \text { (6 outcomes) }$$
Or
$$P(A \cap B)=P(A \mid B) P(B)$$

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

When we toss a die the outcome is one of six numbers, ‘ 1 ‘, $\ldots$, ‘ 6 ‘. We now define these numbers as a variable $X$ (by convention, an uppercase letter), in the sense that the variable $X$ will take on one of these six numbers. However we cannot definitely say which of these numbers will appear. Therefore $X$ is given the name ‘random variable’.

The notation which will be adopted is that the random $X$ takes on the value of $x \in{1,2 \ldots 6}$, which is the sample space $\mathcal{S}$. In this case we are dealing with a discrete random variable. A second example is the length of screws produced in a factory where the nominal length of the screw may be, for example, $1 \mathrm{~cm}$, and the random variable $L$ (the length of the screw) will take on values of $l \in \mathcal{S}=$ {interval, $\left.\left(0, L_{\max }\right)\right}$ where $L_{\max }$ is a large number which is envisaged to be the maximum value which $L$ may take, though $L$ will almost always take on values around $1 \mathrm{~cm}$. In this case the random variable $L$ will take on continuous values. These two sample spaces are shown in Fig. 3.4.

电气工程代写模拟和数字通信代写ANALOGUE AND DIGITAL COMMUNICATIONS代考|CONDITIONAL PROBABILITY AND INDEPENDENT EVENTS

$A=(1,1) \ldots(1,6) \quad$ (6 outcomes) $\quad B=(1,2),(2,2), \ldots(6,2) \quad$ (6 outcomes)

$$A \cap B=(1,2) P(A \cap B) \quad=\frac{1}{36}$$

readas” “probabilityofoccurrenceoftheevent $\$ A \$$given \ B \$$ hasoccurred由于样本空间
$$A \mid B=(1,2),(2,2) \ldots(6,2) \quad \text { (6 outcomes) }$$

$$P(A \cap B)=P(A \mid B) P(B)$$

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。