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统计代写|概率与统计代考Probability and Statistics代写|MATH352 INTRODUCTION

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统计代写|概率与统计代考Probability and Statistics代写|INTRODUCTION

Consider a situation where we want to evaluate the probability $P(A)$ of some event $A$. Suppose that after finding $P(A)$, we learn that some other event, $B$, occurred. In many cases, such an information leads to a change in the assessment of the probability of the event $A$. The symbol used for this new probability will be $P(A \mid B)$, to be read “conditional probability of $A$, given $B$,” or “probability of event $A$, given that $B$ occurred.”
EXAMPLE $4.1$
Conditional probabilities are most easily interpreted as probabilities in subpopulations. Consider an attribute such as color blindness, known to occur much more often among men than among women. If $D$ is the event “a randomly selected person is color blind,” then $P(D)$ refers to the chance of color blindness in the whole population. Suppose now that the person selected is known to be a woman (event $W$ ). This information changes the assessment of probability of color blindness to $P(D \mid W)$, which is now the probability of color blindness in the subpopulation of women.
Questions that might arise here are the following:

How to use data on probabilities of color blindness separately among men and women to find the overall chance of color blindness, that is, to find $P(D)$ if we know $P(D \mid W)$ and $P(D \mid M)$ ?

How to find the probability that a randomly selected color blind person is a woman, that is, $P(W \mid D)$ ?

The first of these questions requires using the weighted average, usually referred to as the formula for total probability (Section 4.3). To answer the second question, one has to use the Bayes’ formula (Section 4.4).
The examples and exercises in this chapter are designed to provide practice in recognizing which probabilities are conditional and which are not.

统计代写|概率与统计代考Probability and Statistics代写|PROBLEMS

A computer file contains data on households in a certain city. Each entry line in this file contains various information about one household: income, socioeconomic status, number of children, their ages, and so on. One data line can then be selected at random (each line has the same probability of being selected). Consequently, probabilities of various events are interpretable as relative frequencies of entries in the data file with the corresponding property.

Let $X, Y$, and $Z$ be, respectively, the numbers of boys, girls, and cars in the households sampled. Let $A$ be the event that a household has a TV set, and let $B$ be the event that it has a swimming pool.
(i) Interpret the probabilities below as relative frequencies of occurrence of some attributes in certain subpopulations. (a) $P(A)$. (b) $P(A \mid Z>0)$. (c) $P(Z>0 \mid A)$. (d) $P(X=0 \mid X+Y=3)$. (e) $P\left(B \mid A^c\right)$. (f) $P\left[(X+Y=0)^c \mid A \cap B\right]$. (g) $P(X Y=$ $0 \mid X+Y>1)$
(ii) Use symbols to express probabilities corresponding to the following relative frequencies: (a) Relative frequency of households with two cars. (b) Relative frequency of households with no children among households with at least one car. (c) Relative frequency of households that have both a swimming pool and a TV set, among those who have either a swimming pool or a TV set and have at least one car.

概率与统计代写

统计代写|概率与统计代考概率统计代写|简介

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EXAMPLE $4.1$

统计代写|概率与统计代考概率与统计代写|PROBLEMS

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(ii)用符号表示对应于下列相对频率的概率:(a)拥有两辆汽车的家庭的相对频率。(b)至少拥有一辆汽车的家庭中没有子女的家庭的相对频率。(c)同时拥有游泳池和电视机的家庭的相对频率，在那些既拥有游泳池又拥有电视机并且至少拥有一辆汽车的家庭中

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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。