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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
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• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
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## 统计代写|生物统计代写Biostatistics代考|Parameters for Bivariate Populations

In most biomedical research studies, there are many variables that will be recorded on each individual in the study. A multivariate distribution can be formed by jointly tabulating, charting, or graphing the values of the variables over the $N$ units in the population. For example, the bivariate distribution of two variables, say $X$ and $Y$, is the collection of the ordered pairs
$$\left(X_1, Y_1\right),\left(X_2, Y_2\right),\left(X_3, Y_3\right), \ldots,\left(X_N, Y_N\right) .$$
These $N$ ordered pairs form the units of the bivariate distribution of $X$ and $Y$ and their joint distribution can be displayed in a two-way chart, table, or graph.

When the two variables are qualitative, the joint proportions in the bivariate distribution are often denoted by $p_{a b}$, where
$$p_{a b}=\text { proportion of pairs in population where } X=a \text { and } Y=b$$
The joint proportions in the bivariate distribution are then displayed in a two-way table or two-way bar chart. For example, according to the American Red Cross, the joint distribution of blood type and Rh factor is given in Table $2.7$ and presented as a bar chart in Figure $2.21$.

In a bivariate distribution where one of the variables is quantitative and the other is qualitative, the best way to graphically present the distribution is to separate the distribution into subpopulations according to the values of the qualitative distribution. For example, if $W=$ the weight of an individual and $G=$ the sex of an individual, then the best way to present the bivariate distribution of weight and gender is to present the two subpopulations separately as shown in Figure 2.22.

In a multivariate population, the subpopulations remain important, and the individual subpopulation proportions, percentiles, mean, median, modes, standard deviation, variance, interquartile range are important parameters that can still be used to summarize each of the subpopulations.

In a bivariate distribution where both of the variables are quantitative, a threedimensional graph can be used to represent the joint distribution of the variables. The joint distribution is displayed as a three-dimensional probability density graph with one axis for each of the variables and the third axis representing the joint density at each pair $(X, Y)$; however, three-dimensional density plots are sometimes difficult to interpret. An example of a three-dimensional density plot is given in Figure 2.23.

## 统计代写|生物统计代写Biostatistics代考|PROBABILITY

In a data-based biomedical study, a random sample will be selected from the target population and a well-designed sampling plan requires knowing the chance of drawing a particular observation or set of observations. For example, it might be important to know the chance of drawing a female individual or an individual between the ages of 30 and 60 . In other studies, it might be important to determine the likelihood that a particular genetic trait will be passed from the parents to their offspring.

A probability is a number between 0 and 1 that measures how likely it is for an event to occur. Probabilities are associated with tasks or experiment where the outcome cannot be determined without actually carrying out the task. A task where the outcome cannot be predetermined is called a random experiment or a chance experiment. For example, prior to treatment it cannot be determined whether chemotherapy will improve a cancer patient’s health. Thus, the result of a chemotherapy treatment can be treated as a chance experiment before chemotherapy is started. Similarly, when drawing a random sample from the target population, the actual values of the sample will not be known until the sample is actually collected. Hence, drawing a random sample from the target population is a chance experiment.

Because statistical inferences are based on a sample from the population rather than a census of the population, the statistical inferences will have a degree of uncertainty associated with them. The measures of reliability for statistical inferences drawn from a sample are based on the underlying probabilities associated with the target population.

In a chance experiment, the actual outcome of the experiment cannot be predetermined, but it is important for the experimenter to identify all of the possible outcomes of the experiment before it is carried out. The set of all possible outcomes of a chance experiment is called the sample space and will be denoted by $\mathcal{S}$. A subcollection of the outcomes in the sample space is called an event, and the probability of an event measures how likely the event is. An event is said to occur when a chance experiment is carried out and the chance experiment results in one of the outcomes in the event. For example, in a chance experiment consisting of randomly selecting an adult from a well-defined population, if $A$ is the event that an individual between the ages of 30 and 60 is selected. then the event $A$ will occur if and only if the age of the individual selected is between 30 and 60 ; if the age of the individual is not between 30 and 60 , then the event $A$ will not occur.

# 生物统计代考

## 统计代写|生物统计代写Biostatistics代考|Parameters for Bivariate Populations

(X1,是1),(X2,是2),(X3,是3),…,(Xñ,是ñ).

p一个b= 人口中对的比例 X=一个 和 是=b

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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。