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assignmentutor-lab™ 为您的留学生涯保驾护航 在代写线性代数linear algebra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。我们的专家在代写线性代数linear algebra代写方面经验极为丰富，各种代写线性代数linear algebra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

## 数学代写|线性代数代写linear algebra代考|Binomial Distribution

For the remainder of this chapter, we are going to learn two probability distributions: the binomial and beta distributions. While we will not be using these for the rest of the book, they are useful tools in themselves and fundamental to understanding how events occur given a number of trials. They will also be a good segue to understanding probability distributions that we will use heavily in Chapter 3 . Let’s explore a use case that could occur in a real-world scenario.

Let’s say you are working on a new turbine jet engine and you ran 10 tests. The outcomes yielded eight successes and two failures:
$$\checkmark \checkmark \checkmark \checkmark \times \checkmark x \checkmark \checkmark$$
You were hoping to get a $90 \%$ success rate, but based on this data you conclude that your tests have failed with only $80 \%$ success. Each test is time-consuming and expensive, so you decide it is time to go back to the drawing board to reengineer the design.

However, one of your engineers insists there should be more tests. “The only way we will know for sure is to run more tests,” she argues. “What if more tests yield $90 \%$ or greater success? After all, if you flip a coin 10 times and get 8 heads, it does not mean the coin is fixed at $80 \%$.”

You briefly consider the engineer’s argument and realize she has a point. Even a fair coin flip will not always have an equally split outcome, especially with only 10 flips. You are most likely to get five heads but you can also get three, four, six, or seven heads. You could even get 10 heads, although this is extremely unlikely. So how do you determine the likelihood of $80 \%$ success assuming the underlying probability is $90 \% ?$

One tool that might be relevant here is the binomial distribution, which measures how likely $k$ successes can happen out of $n$ trials given $p$ probability.
Visually, a binomial distribution looks like Figure 2-1.
Here, we see the probability of $k$ successes for each bar out of 10 trials. This binomial distribution assumes a probability $p$ of $90 \%$, meaning there is a $.90$ (or $90 \%$ ) chance for a success to occur. If this is true, that means there is a .1937 probability we would get 8 successes out of 10 trials. The probability of getting 1 success out of 10 trials is extremely unlikely, .000000008999, hence why the bar is not even visible.

We can also calculate the probability of eight or fewer successes by adding up bars for eight or fewer successes. This would give us $.2639$ probability of eight or fewer successes.

## 数学代写|线性代数代写linear algebra代考|Beta Distribution

What did I assume with my engine-test model using the binomial distribution? Is there a parameter I assumed to be true and then built my entire model around it? Think carefully and read on.

What might be problematic about my binomial distribution is I assumed the underlying success rate is $90 \%$. That’s not to say my model is worthless. I just showed if the underlying success rate is $90 \%$, there is a $26.39 \%$ chance I would see 8 or fewer successes with 10 trials. So the engineer is certainly not wrong that there could be an underlying success rate of $90 \%$.

But let’s flip the question and consider this: what if there are other underlying rates of success that would yield $8 / 10$ successes besides $90 \%$ ? Could we see $8 / 10$ successes with an underlying $80 \%$ success rate? $70 \%$ ? $30 \%$ ? When we fix the $8 / 10$ successes, can we explore the probabilities of probabilities?

Rather than create countless binomial distributions to answer this question, there is one tool that we can use. The beta distribution allows us to see the likelihood of different underlying probabilities for an event to occur given alpha successes and beta failures.

# 线性代数代考

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## 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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师