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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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
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## 统计代写|生物统计代写Biostatistics代考|Basic Probability Rules

Determining the probabilities associated with complex real-life events often requires a great deal of information and an extensive scientific understanding of the structure of the chance experiment being studied. In fact, even when the sample space and event are easily identified, the determination of the probability of an event can be an extremely difficult task. For example, in studying the side effects of a drug, the possible side effects can generally be anticipated and the sample space will be known. However, because humans react differently to drugs, the probabilities of the occurrence of the side effects are generally unknown. The probabilities of the side effects are often estimated in clinical trials.

The following basic probability rules are often useful in determining the probability of an event.

1. When the outcomes of a random experiment are equally likely to occur, the probability of an event $A$ is the number of outcomes in $A$ divided by the number of simple events in $\mathcal{S}$. That is,
$$P(A)=\frac{\text { number of simple events in } A}{\text { number of simple events in } \mathcal{S}}=\frac{N(A)}{N(\mathcal{S})}$$
2. For every event $A$, the probability of $A$ is the sum of the probabilities of the outcomes comprising $A$. That is, when an event $A$ is comprised of the outcomes $O_1, O_2, \ldots, O_k$, the probability of the event $A$ is
$$P(A)=P\left(O_1\right)+P\left(O_2\right)+\cdots+P\left(O_k\right)$$
3. For any two events $A$ and $B$, the probability that either event $A$ or event $B$ occurs is
$$P(A \text { or } B)=P(A)+P(B)-P(A \text { and } B)$$
4. The probability that the event $A$ does not occur is 1 minus the probability that the event $A$ does ossur. That is.
$$P(A \text { does not occur })=1-P(A)$$

## 统计代写|生物统计代写Biostatistics代考|Conditional Probability

In many biomedical studies, the probabilities associated with a qualitative variable will be modeled. A good probability model will take into account all of the factors believed to cause or explain the occurrence of the event. For example, the probability of survival for a melanoma patient depends on many factors including tumor thickness, tumor ulceration, gender, and age. Probabilities that are functions of a particular set of conditions are called conditional probabilities.

Conditional probabilities are simply probabilities based on well-defined subpopulations defined by a particular set of conditions (i.e., explanatory variables). The conditional probability of the event $A$ given that the event $B$ has occurred is denoted by $P(A \mid B)$ and is defined as
$$P(A \mid B)=\frac{P(A \cap B)}{P(B)}$$
provided that $P(B) \neq 0$. Specifying that the event $B$ has occurred places restrictions on the outcomes of the chance experiment that are possible. Thus, the outcomes in the event $B$ become the subpopulation upon which the probability of the event $A$ is based,
Example 2.22
Suppose that in a population of 100 units 35 units are in event $A, 48$ of the units are in event $B$, and 22 units are in both events $A$ and $B$. The unconditional probability of event $A$ is $P(A)=\frac{35}{m 11}=0.35$. The conditional probability of event $A$ given that event $B$ has occurred is
$$P(A \mid B)=\frac{0.22}{0.48}=0.46$$
In this example, knowing that event $B$ has occurred increases the probability that event $A$ will occur from $0.35$ to $0.46$. That is, event $A$ is more likely to occur if it is known that event $B$ has occurred.
Since conditional probabilities are probabilities, the rules associated with conditional probabilities are similar to the rules of probability. In particular,

1. conditional probabilities are always between 0 and 1 . That is, $0 \leq P(A \mid B) \leq 1$.
2. $P($ A does not occur $\mid B)=1-P(A \mid B)$.
3. $P(A$ or $B \mid C)=P(A \mid C)+P(B \mid C)-P(A$ and $B \mid C)$.
Conditional probabilities play an important role in the detection of rare diseases and the development of screening tests for diseases. Two important conditional probabilities used in disease detection are the sensitivity and specificity. The sensitivity is defined to be the conditional probability of a positive test for the subpopulation of individuals having the disease (i.e., $P(+\mid D)$ ), and the specificity is defined to be the conditional probability of a negative test for the subpopulation of individuals who do not have the disease (i.e., $P(-\mid$ not $D))$. Thus, the sensitivity of a diagnostic test measures the accuracy of the test for a individual having the disease, and the specificity measures the accuracy of the test for individuals who do not have the disease.

# 生物统计代考

## 统计代写|生物统计代写Biostatistics代考|Basic Probability Rules

1. 当随机实验的结果同样可能发生时，事件发生的概率 $A$ 是结果的数量 $A$ 除以简单事件的数量 $\mathcal{S}$. 那是，
$$P(A)=\frac{\text { number of simple events in } A}{\text { number of simple events in } \mathcal{S}}=\frac{N(A)}{N(\mathcal{S})}$$
2. 对于每一个事件 $A_i$ 的概率 $A$ 是结果的概率之和，包括 $A$. 也就是说，当一个事件 $A$ 由结果组成 $O_1, O_2, \ldots, O_k$ 事件的概率 $A$ 是
$$P(A)=P\left(O_1\right)+P\left(O_2\right)+\cdots+P\left(O_k\right)$$
3. 对于任意两个事件 $A$ 和 $B$ ，任一事件的概率 $A$ 或事件 $B$ 发生是
$$P(A \text { or } B)=P(A)+P(B)-P(A \text { and } B)$$
4. 事件发生的概率 $A$ 不发生是 1 减去事件发生的概率 $A$ 做ossur。那是。
$$P(A \text { does not occur })=1-P(A)$$

## 统计代写|生物统计代写Biostatistics代考|Conditional Probability

$$P(A \mid B)=\frac{P(A \cap B)}{P(B)}$$

$$P(A \mid B)=\frac{0.22}{0.48}=0.46$$

1. 条件概率始终介于 0 和 1 之间。那是， $0 \leq P(A \mid B) \leq 1$.
2. $P(\mathrm{~A}$ 不发生 $\mid B)=1-P(A \mid B)$.
3. $P(A$ 或者 $B \mid C)=P(A \mid C)+P(B \mid C)-P(A$ 和 $B \mid C)$.
条件概率在罕见疾病的检测和疾病筞查测试的开发中发挥着重要作用。用于疾病检测的两个重要条件概率是敏感性和特异性。敏感性被定义为对恵有该疾 病的个体亚群（即， $P(+\mid D)$ )，特异性被定义为对没有患病的个体亚群（即， $P(-\mid$ 不是 $D)$ ). 因此，诊断测试的敏感性衡量的是对恵有疾病的个体进行 测试的准确性，而特异性衡量的是对末患有疾病的个体进行测试的准确性。

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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。