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# 数学网课代修|概率统计代写PROBABILITY AND STATISTICS代考|MATHS2103 HEIGHTS OF UNION SOLDIERS

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## 数学网课代修|概率统计代写PROBABILITY AND STATISTICS代考|HEIGHTS OF UNION SOLDIERS

Figure 2.9 shows the height of more than 20,000 Union soldiers at the time of the Civil War. The area in the histogram covering the interval of heights from $65.0$ inches to just below $67.0$ inches has been shaded dark grey. Of them 5578 soldiers were in this height range – that is, $27.6 \%$ of all the soldiers in the sample. The green area occupies $27.6 \%$ of the area of the histogram. The probability of any soldier chosen at random being within this height interval would be $0.276$. This is another empirical distribution, but it conforms very closely to what a Gaussian distribution would lead us to expect. The survey was organised by Benjamin Gould, one of the founders of the US National Academy of Science in 1863, an astronomer, and amongst his many other scientific roles, actuary to the US Sanitary Commission, who in the face of often-determined bureaucratic resistance collected and tabulated the vital statistics of troops in order to test ‘those hygienic and physiological laws which are already known’ and ‘to discover and apply such other laws as might affect the welfare and success of our soldiers’ (Comstock, 1922, p. 162). The data he compiled proved an immensely valuable resource in the study of health, demography and many other fields. Soldiers’ heights were measured to the nearest half inch. The mean height of the 20,207 soldiers he studied was 67 inches and the standard deviation found to be $2.58$ inches. We might therefore expect to see a total of around $0.05^{*} 20207 \approx 1010$ soldiers who were either taller than $67+1.96 * 2.58=72$ inches or shorter than $67-$ $1.96 * 2.58=62$ inches. Gould observed 1055 such soldiers, remarkably close to what we might expect if height followed a perfectly Gaussian distribution.

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

By now, it should have become clear that probability distributions and variables are the same beast. Each variable describes a trial with a sample space. The values of variables correspond to the trial outcomes in the sample space for that variable. Each observation or case is one instance of that trial. This raises the question ‘How do we ensure that the trials are identical and independent?’ If they were not identical and independent, there would be no point in their repetition because we would have no means either of comparing them or of calculating the results obtained from more than one trial. It would be rather like trying to add apples and bicycles together. If I flip a coin a few times, I can reasonably claim to be repeating an identical and independent trial. But in what way is asking a collection of different people a survey question the repetition of an identical and independent trial? I must be able to claim that the respondents share something in common that gives them the same status as the virtual coin I flipped, and that it is this that I can make probability statements about, just as I could about the coin. What they have in common is membership of a target population. Just as my probability statements about coin flips refer to the coin, and not to any individual outcome from a flip, so too do my statements about survey respondents, whether expressed as proportions or probabilities, refer to them as a group and not to individual members of that group. The target population can be $48 \%$ male. My probability of picking a man at random from it can be $0.48$, but there are no individuals in it who are $48 \%$ male, or $67 \%$ agree with a statement or possess precisely the mean age, income or height of the target population. Neither are there individual soldiers who have $2.5 \%$ of their height above 6 feet, or babies whose individual weight has any standard deviation.

## 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。