数学代写|线性代数代写linear algebra代考|МATH 1014

2022年7月13日

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数学代写|线性代数代写linear algebra代考|Populations, Samples, and Bias

Before we dive deeper into descriptive and inferential statistics, it might be a good idea to lay out some definitions and relate them to tangible examples.

A population is a particular group of interest we want to study, such as “all seniors over the age of 65 in the North America,” “all golden retrievers in Scotland,” or “current high school sophomores at Los Altos High School.” Notice how we have boundaries on defining our population. Some of these boundaries are broad and capture a large group over a vast geography or age group. Others are highly specific and small such as the sophomores at Los Altos High School. How you hone in on defining a population depends on what you are interested in studying.

A sample is a subset of the population that is ideally random and unbiased, which we use to infer attributes about the population. We often have to study samples because polling the entire population is not always possible. Of course, some populations are easier to get hold of if they are small and accessible. But measuring all seniors over 65 in North America? That is unlikely to be practical!

It is important to note that populations can be theoretical and not physically tangible. In these cases our population acts more like a sample from something abstract. Here’s my favorite example: we are interested in flights that depart between 2 p.m. and 3 p.m. at an airport, but we lack enough flights at that time to reliably predict how often these flights are late. Therefore, we may treat this population as a sample instead from an underlying population of all theoretical flights taking off between 2 p.m. and 3 p.m.

Problems like this are why many researchers resort to simulations to generate data. Simulations can be useful but rarely are accurate, as simulations capture only so many variables and have assumptions built in.

数学代写|线性代数代写linear algebra代考|Mean and Weighted Mean

The mean is the average of a set of values. The operation is simple to do: sum the values and divide by the number of values. The mean is useful because it shows where the “center of gravity” exists for an observed set of values.

The mean is calculated the same way for both populations and samples. Example 3-1 shows a sample of eight values and how to calculate their mean in Python.
Example 3-1. Calculating mean in Python

Number of pets each person owns

sample $=[1,3,2,5,7,0,2,3]$
mean $=$ sum(sample) $/$ len(sample)
print(mean) # prints $2.875$
As you can see, we polled eight people on the number of pets they own. The sum of the sample is 23 and the number of items in the sample is 8 , so this gives us a mean of $2.875$ as $23 / 8=2.875$.

There are two versions of the mean you will see: the sample mean $\bar{x}$ and the population mean $\mu$ as expressed here:
\begin{aligned} &\bar{x}=\frac{x_{1}+x_{2}+x_{3}+\ldots+x_{n}}{n}=\sum \frac{x_{i}}{n} \ &\mu=\frac{x_{1}+x_{2}+x_{3}+\ldots+x_{n}}{N}=\sum \frac{x_{i}}{N} \end{aligned}

线性代数代考

数学代写|线性代数代写linear algebra代考|Mean and Weighted Mean

print(mean) # 打印 $2.875$

$\bar{x}=\frac{x_{1}+x_{2}+x_{3}+\ldots+x_{n}}{n}=\sum \frac{x_{i}}{n} \quad \mu=\frac{x_{1}+x_{2}+x_{3}+\ldots+x_{n}}{N}=\sum \frac{x_{i}}{N}$

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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。