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• 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

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|The Monty Hall Problem

Recall that we have three doors, behind which one has a valuable prize and two have something worthless. After the contestant chooses one of the three doors Monty Hall (who knows which door has the prize behind it) always reveals a door (other than the one chosen) that has a worthless item behind it. The contestant can now choose to switch doors or stick to his or her original choice. The sensible decision is always to switch because doing so increases your probability of winning from $1 / 3$ to $2 / 3$ compared to sticking with the original choice. There are many explanations of this but we feel the following (shown graphically in Figure 5.9) is the easiest to understand.

The key thing to note is that Monty Hall will always choose a door without the prize, irrespective of what your choice is. So consequently the event “door first chosen wins” is independent of Monty Hall’s choice. This means that the probability of the event “door first chosen wins” is the same as the probability of this event conditional on Monty Hall’s choice. Clearly, when you first choose, the probability of choosing the winning door is $1 / 3$. Since Monty Hall’s choice of doors has no impact on this probability, it remains $1 / 3$ after Monty Hall makes his choice. So, if you stick to your first choice the probability of winning stays at $1 / 3$; nothing that Monty Hall does can change this probability.

Since there is a $1 / 3$ probability that your first choice is the prizewinning door, it follows that the probability that your first choice is not the prize-winning door is $2 / 3$. But if your first choice is not the prize-winning door then you are guaranteed to win by switching doors. That is because Monty Hall always reveals a door without the prize (so, for example, if you chose door 1 and the prize is behind door 2 Monty Hall would have to reveal door 3 , which has no prize). So, since you always win by switching in the case where your first choice was not the prize-winning door, there is a $2 / 3$ probability of winning by switching.

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|When Incredible Events Are Really Mundane

The birthdays problem is a classic example of a very common fallacy of probabilistic reasoning, namely, to underestimate the true probability of an event that seems to be unlikely. More dramatic examples appear in the media all the time. You will all have come across newspaper articles and television reports of events that are reported to be one in a million, one in a billion, or maybe even one in a trillion. But it is usually the case that the probability of such events is much higher than stated. In fact, it is often the case that such events are so common that it would be more newsworthy if it did not happen.
Example 5.21
A few years ago the Sun newspaper carried a story about a woman who had just given birth to her eighth child, all of whom were boys. It said that the probability of this happening was less than one in a billion.

The fallacy here, as in all such stories, is to confuse the specific with the general. The probability of a specific mother (for example, your mother) giving birth this year to her eighth child, all of which are boys, is indeed very low (as we will explain later). But the probability of this happening to at least one mother in the United Kingdom during a one-year period is almost a certainty. Why?

In any given year there are approximately 700,000 births in the United Kingdom. Among these approximately 1000 are to mothers having their eighth child. Now, in a family of eight children, the probability that all eight are boys is 1 in 256; this was explained in Example $5.19$ using the Binomial distribution. So there is a probability of $1 / 256$ that a mother having her eighth child will have all boys. So, out of 1000 such mothers how many will have all boys? This is another case of the Binomial distribution, this time with $n=1000$ and $p=1 / 256$. The probability that none of the 1000 mothers have all hnys is
$$\left(\frac{255}{256}\right)^{1000}=0.01996$$

# 贝叶斯分析代考

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|When Incredible Events Are Really Mundane

$$\left(\frac{255}{256}\right)^{1000}=0.01996$$

## 有限元方法代写

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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。

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