Posted on Categories:Statistical inference, 统计代写, 统计代考, 统计推断

# 统计代写|统计推断代考Statistical Inference代写|The Lottery Problem or Rare Things Are Common

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## 统计代写|统计推断代考Statistical Inference代写|The Lottery Problem or Rare Things Are Common

This problem is identical to the birthday problem mathematically, with the only difference that the probability numbers are much smaller and the number of participants is much larger. We start with a story about someone winning the lottery twice in the same day! ${ }^2$
Can you imagine winning the lottery twice in one day?
Angelo and Maria Gallina don’t have to imagine – they hit twice on Nov. 20.

The married couple from Belmont, Calif., had separately bought tickets in two different California state lottery games, and both could hardly believe their eyes as all 11 winning numbers over two games came up….Before taxes, their winnings amounted to $\$ 126$,000 for the Fantasy 5 and$\$17$ million for the SuperLotto Plus, according to The Associated Press…Orkin arrived at the number by multiplying the roughly 41-million-to-one odds of winning the SuperLotto game and the 575, ,000-to-one odds of winning the Fantasy 5 game to arrive at odds of 23,575,000,000,000-to-one.
Pretty amazing! That’s something like
$$P(\text { winning two tickets })=\frac{1}{2 \cdot 10^{13}} \sim 5 \cdot 10^{-14}$$
which truly is quite improbable as a single event, but is it truly an improbable event to happen somewhere? The assumption stated in the quote is that only two tickets were purchased. We all know that many lottery tickets are purchased daily, which should increase the chance that somewhere this will occur. Even this winning couple purchased tickets every day for 20 years before winning this.

## 统计代写|统计推断代考Statistical Inference代写|Monty Hall Problem

One of the most popular probability problems is called the Monty Hall problem, and is based on the television game show “Let’s Make a Deal.”3 It can take on many forms, but a common form is as follows 4

Example 2.14 Suppose you’re on a game show, and you’re given the choice of three doors: behind one door is a car; behind the others, goats. You pick a door, say No. I (but the door is not opened), and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to change your choice to door No. 2?” Is it to your advantage or disadvantage to switch your choice, or does it matter whether you switch your choice or not?
The result is that it is always better to switch, where the probability of getting the car moves up from $1 / 3$ to $2 / 3$ by switching! Because this problem is particularly unintuitive, we will break it up into smaller pieces. The critical aspect of this is that a change in our assignment of probability to an event must be somehow tied to a change in our information about that event. In order to understand the problem, we must then understand where the extra information is coming from.
We will step up to the full problem listed, but for now we explore some simpler versions of the problem.

EXAMPLE 2.15 Imagine we have a game with two doors: Behind one door is a car; behind the other is a goat. You pick a door, say No. 1 (but the door is not opened), and the host, who knows what’s behind the doors, says that there is a $90 \%$ chance that the car is behind door No. 2. Is it to your advantage to switch your choice?

Initially there is a two-door choice, with no information about either choice, so we assign equal probabilities to the choices: $P$ (car behind No. 1$)=$ $P($ car behind No. 2) $=0.5$ (i.e. a 50-50 chance). After the host gives information, this changes. Although this is still a two-door choice, it is no longer a 50-50 chance. By having a knowledgable person give you information suddenly changes the situation to a 10-90 chance, and it is much better for you to switch.

# 统计推断代写

## 统计代写|统计推断代考Statistical Inference代写|The Lottery Problem or Rare Things Are Common

$$P(\text { winning two tickets })=\frac{1}{2 \cdot 10^{13}} \sim 5 \cdot 10^{-14}$$

## 统计代写|统计推断代考Statistical Inference代写|Monty Hall Problem

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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。