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# 数学网课代修|概率统计代写PROBABILITY AND STATISTICS代考|MAT130 THE PROBABILITY DISTRIBUTION

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## 数学网课代修|概率统计代写PROBABILITY AND STATISTICS代考|THE PROBABILITY DISTRIBUTION

We have seen that any individual outcome of large numbers of repeated trials tends towards a limit that represents the underlying probability of that outcome, expressed as a proportion between 0 and 1 . It follows from our definition of a trial, that the sum of these proportions for each outcome in the sample space must be exactly one. Something must happen in each trial. The total of all the outcomes must therefore equal the total number of trials. The relative frequency of each outcome in the sample space in any series of trials will therefore be the proportion or times they occur and equal to their probability. We can therefore display the outcomes of a trial that has been repeated as a distribution showing the frequency of each outcome in the sample space. We can produce a frequency table if outcomes are discrete or summary statistics (like the mean, median, standard deviation or IQR) if the outcome is continuous. We can also represent this distribution visually using bar charts or histograms.
Table $2.2$ is a frequency table based on results from the eighth round of the European Social Survey showing the sex of respondents. There were 52,142 identical repeated independent trials comprising the question about the sex of the respondent. Of them, 24,948 respondents said that they were male, which is $0.478$ of all the trials. We could describe the probability of that outcome as $p=0.478$. This does not mean than that anyone in the survey was $47.8 \%$ male. Our probability refers to the series of all the repeated trials, not the result of any individual trial. It does mean that if we selected anyone at random from all the respondents, we would have a long-run probability of $47.8 \%$ of picking a man. We would have a $p=0.522$ of picking a woman. And because these two outcomes described the complete sample space, we would have $0.478+0.522=1=$ the absolute certainty of picking either a man or a woman.

## 数学网课代修|概率统计代写PROBABILITY AND STATISTICS代考|BAR CHARTS AND HISTOGRAMS

Probability distributions can be displayed visually using the following rule. The proportion of the total area of the chart that represents each outcome is the same as the probability of that outcome in the sample space. For bar charts, as long as the bars are of equal width, this means that their height is proportional to the probability, or to the frequency (since the frequency of each outcome divided by the total number of trials is the same as the probability). Figure $2.7$ shows our example of attitudes to homosexuality, with the refusals and don’t knows excluded. At a glance, we can see that most people agree with the statement.

## 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。