## 数学网课代修|概率统计代写Probability and Statistics代考|MATH 200

statistics-lab™ 为您的留学生涯保驾护航 在代写概率统计Probability and Statistics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统计Probability and Statistics代写方面经验极为丰富，各种代写概率统计Probability and Statistics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

## 数学网课代修|概率统计代写Probability and Statistics代考|ALOHA Network

In this section, an example from computer networks is presented which, as with the bus ridership example, will be used at a number of points in this book. Probability analysis is used extensively in the development of new, faster types of networks.

We speak of nodes on a network. These might be computers, printers or other equipment. We will also speak of messages; for simplicity, let’s say a message consists of a single character. If a user at a computer hits the $\mathrm{N}$ key, say, in a connection with another computer, the user’s machine sends the ASCII code for that character onto the network. Of course, this was all transparent to the user, actions behind the scenes.

Today’s Ethernet evolved from an experimental network developed at the University of Hawaii, called ALOHA. A number of network nodes would occasionally try to use the same radio channel to communicate with a central computer. The nodees couldn’t hear éach otherr, dué to the obstruction of mountains between them. If only one of them made an attempt to send, it would be successful, and it would receive an acknowledgement message in response from the central computer. But if more than one node were to transmit, a collision would occur, garbling all the messages. The sending nodes would timeout after waiting for an acknowledgement that never came, and try sending again later. To avoid having too many collisions, nodes would engage in random backoff, meaning that they would refrain from sending for a while even though they had something to send.

## 数学网课代修|概率统计代写Probability and Statistics代考|ALOHA in the Notebook Context

Think of doing the ALOHA “experiment” many, many times. Let’s interpret the numbers we found above, e.g., $P\left(X_{1}=2\right)=0.52$, in the notebook context.

• Run the network for two epochs, starting with both nodes active, the first time, and write the outcome on the first line of the notebook.
• Run the network for two epochs, starting with both nodes active, the second time, and write the outcome on the second line of the notebook.
• Run the network for two epochs, starting with both nodes active, the third time, and write the outcome on the third line of the notebook.
• Run the network for two epochs, starting with both nodes active, the fourth time, and write the outcome on the fourth line of the notebook.
• Imagine you keep doing this, thousands of times, filling thousands of linés in thé notebbook.

Thẻ first seveen linés of thè notẻbook might look liké Táblè1.3. Wé seee that:

• Among those first seven lines in the notebook, 4/7 of them have $X_{1}=2$. After many, many lines, this fraction will be approximately $0.52$.
• Among those first seven lines in the notebook, $3 / 7$ of them have $X_{2}=2$. After many, many lines, this fraction will be approximately $0.47 .{ }^{7}$
• Among those first seven lines in the notebook, $2 / 7$ of them have $X_{1}=2$ and $X_{2}=2$. After many, many lines, this fraction will be approximately $0.27 .$
• Among the first seven lines in the notebook, four of them do not say NA in the $X_{2}=2 \mid X_{1}=2$ column. Among these four lines, two say Yes, a fraction of $2 / 4$. After many, many lines, this fraction will be approximately $0.52$.

## 数学网课代修|概率统计代写Probability and Statistics代考|ALOHA in the Notebook Context

• 将网络运行两个 epoch，第一次从两个节点都处于活动状态开始，并将结果写在笔记本的第一行。
• 将网络运行两个 epoch，第二次从两个节点都处于活动状态开始，并将结果写在笔记本的第二行。
• 运行网络两个 epoch，从两个节点开始，第三次，并将结果写在笔记本的第三行。
• 运行网络两个 epoch，从两个节点开始，第四次，并将结果写在笔记本的第四行。
• 想象一下，你不断地这样做，数千次，在笔记本中填满数千行。

thè notẻbook 的前七行可能看起来像 Táblè1.3。我们看到：

• 在笔记本的前七行中，有 4/7X1=2. 在很多很多行之后，这个分数将大约为0.52.
• 在笔记本的前七行中，3/7其中有X2=2. 在很多很多行之后，这个分数将大约为0.47.7
• 在笔记本的前七行中，2/7其中有X1=2和X2=2. 在很多很多行之后，这个分数将大约为0.27.
• 笔记本前七行中，有四行没有在X2=2∣X1=2柱子。在这四行中，有两行说是，一小部分2/4. 在很多很多行之后，这个分数将大约为0.52.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 数学网课代修|概率统计代写Probability and Statistics代考|MATH 1342

statistics-lab™ 为您的留学生涯保驾护航 在代写概率统计Probability and Statistics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统计Probability and Statistics代写方面经验极为丰富，各种代写概率统计Probability and Statistics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

## 数学网课代修|概率统计代写Probability and Statistics代考|Theoretical Approaches

In the mathematical theory of probability, we talk of a sample space, which (in simple cases) consists of a list of the possible outcomes $(X, Y)$, seen in Table 1.1. In a theoretical treatment, we place weights of $1 / 36$ on each of the points in the space, reflecting the fact that each of the 36 points is equally likely, and then say, “What we mean by $P(X+Y=6)=\frac{5}{36}$ is that the outcomes $(1,5),(2,4),(3,3),(4,2),(5,1)$ have total weight $5 / 36$.”

Unfortunately, the notion of sample space becomes mathematically tricky when developed for more complex probability models. Indeed, it requires graduate-level math, called measure theory.

And much worse, under the sample space approach, one loses all the intuition. In particular, there is no good way using set theory to convey the intuition underlying conditional probability (to be introduced in Section 1.3). The same is true for expected value, a central topic to be introduced in Section 3.5.

In any case, most probability computations do not rely on explicitly writing down a sample space. In this particular example, involving dice, it is useful for us as a vehicle for explaining the concepts, but we will NOT use it much.

## 数学网课代修|概率统计代写Probability and Statistics代考|Our Definitions

If we were to ask any stranger on the street, “What do we mean when we say that the probability of winning some casino game is $20 \%$ “, she would probably say, “Well, if we were to play the game repeatably, we’d win $20 \%$ of the time.” This is actually the way we will define probability in this book.

The definitions here are intuitive, rather than rigorous math, but intuition is what we need. Keep in mind that we are making definitions below, not a listing of properties.

• We assume an “experiment” which is (at least in concept) repeatable. The above experiment of rolling two dice is repeatable, and even the bus ridership model is so: Each day’s ridership record would be a repetition of the experiment.

On the other hand, the econometricians, in forecasting 2009, cannot “repeat” 2008. Yet all of the econometricians’ tools assume that events in 2008 were affected by various sorts of randomness, and we think of repeating the experiment in a conceptual sense.

• We imagine performing the experiment a large number of times, recording the result of each repetition on a separate line in a note book.
• We say $A$ is an event for this experiment if it is a possible boolean (i.e., yes-or-no) outcome of the experiment. In the above example, here are some events:
\begin{aligned} &* X+Y=6 \ &* X=1 \ &* Y=3 \ &* X-Y=4 \end{aligned}
• A random variable is a numerical outcome of the experiment, such as $X$ and $Y$ here, as well as $X+Y, 2 X Y$ and even $\sin (X Y)$.

## 数学网课代修|概率统计代写Probability and Statistics代考|Our Definitions

• 我们假设一个“实验” (至少在概念上) 是可重复的。上面郑两个骰子的实验是可以重复的，就连公交车的 客流量模型也是如此：每天的客流量记录就是这个实验的重复。
另一方面，计量经济学家在预测 2009 年时，无法“重复” 2008 年。然而，计量经济学家的所有工具都假设 2008 年的事件受到各种随机性的影响，我们认为在概念上重复实验。
• 我们想象进行大量的实验，将每次重复的结果记录在笔记本的单独一行上。
• 我们说 $A$ 如果它是实验的一个可能的布尔 (即，是或否）结果，则它是该实验的事件。在上面的例子中， 这里有一些事件:
$$• X+Y=6 \quad * X=1 * Y=3 \quad * X-Y=4$$
• 随机变量是实验的数值结果，例如 $X$ 和 $Y$ 在这里，以及 $X+Y, 2 X Y$ 乃至 $\sin (X Y)$.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 数学网课代修|概率统计代写Probability and Statistics代考|STA 312

statistics-lab™ 为您的留学生涯保驾护航 在代写概率统计Probability and Statistics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统计Probability and Statistics代写方面经验极为丰富，各种代写概率统计Probability and Statistics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

## 数学网课代修|概率统计代写Probability and Statistics代考|Basic Probability Models

This chapter will introduce the general notions of probability. Most of it will seem intuitive to you, and intuition is indeed crucial in the field of probability and statistics. On the other hand, do not rely on intuition alone; pay careful attention to the general principles which are developed. In more complex settings intuition may not be enough, or may even mislead you. The tools discussed here will be essential, and will be cited frequently throughout the book.

In this book, we will be discussing both “classical” probability examples involving coins, cards and dice, and also examples involving applications in the real world. The latter will involve diverse fields such as data mining, machine learning, computer networks, bioinformatics, document classification, medical fields and so on. Applied problems actually require a bit more work to fully absorb, but needless to say, you will derive the most benefit from those examples rather than ones involving coins, cards and dice. ${ }^{1}$

## 数学网课代修|概率统计代写Probability and Statistics代考|Bus Ridership

Consider the following analysis of bus ridership, which (in more complex form) could be used by the bus company/agency to plan the number of buses, frequency of stops and so on. Again, in order to keep things easy, it will be quite oversimplified, but the principles will be clear.
Here is the model:

• At each stop, each passsenger alights from the bus, independently of the actions of others, with probability $0.2$ each.
• Either 0,1 or 2 new passengers get on the bus, with probabilities $0.5$, $0.4$ and $0.1$, respectively. Passengers at successive stops act independently.
• Assume the bus is so large that it never becomes full, so the new passengers can always board.
• Suppose the bus is empty when it arrives at its first stop.
Here and throughout the book, it will be greatly helpful to first name the quantities or events involved. Let $L_{i}$ denote the number of passengers on the bus as it leaves its $i^{\text {th }}$ stop, $i=1,2,3, \ldots$ Let $B_{i}$ denote the number of new passengers who board the bus at the $i^{\text {th }}$ stop.

Here and throughout the book, it will be greatly helpful to first name the quantities or events involved. Let $L_{i}$ denote the number of passengers on the bus as it leaves its $i^{\text {th }}$ stop, $i=1,2,3, \ldots$ Let $B_{i}$ denote the number of new passengers who board the bus at the $i^{\text {th }}$ stop.

## 数学网课代修|概率统计代写Probability and Statistics代考|Bus Ridership

• 在每一站，每一位乘客从公共汽车上下来，独立于其他人的行动，有概率0.2每个。
• 0,1 或 2 名新乘客上车，概率0.5, 0.4和0.1， 分别。连续停靠的乘客独立行动。
• 假设公共汽车很大以至于它永远不会满员，所以新乘客总是可以上车。
• 假设公共汽车到达第一站时是空的。
在这里和整本书中，首先命名所涉及的数量或事件将非常有帮助。让大号一世表示巴士离开时的乘客人数一世th 停止，一世=1,2,3,…让乙一世表示在一世th 停止。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。