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After completing this reading, you should be able to:
• Explain how a probability matrix can be used to express a probability mass function.
• Compute the marginal and conditional distributions of a discrete bivariate random variable.
• Explain how the expectation of a function is computed for a bivariate discrete random variable.
• Define covariance and explain what it measures.
• Explain the relationship between the covariance and correlation of two
random variables, and how these are related to the independence of the two
variables.
• Explain the effects of applying linear transformations on the covariance and correlation between two random variables.
• Compute the variance of a weighted sum of two random variables.
• Compute the conditional expectation of a component of a bivariate random variable.
• Describe the features of an independent and identically distributed (iid) sequence of random variables.
• Explain how the iid property is helpful in computing the mean and variance of a sum of iid random variables.
完成本阅读后，您应该能够：
•解释如何使用概率矩阵来表示概率质量函数。
•计算离散二元随机变量的边际分布和条件分布。
•解释如何计算二元离散随机变量的函数期望值。
•定义协方差并解释其测量的内容。
•解释两个随机变量的协方差和相关性之间的关系，以及它们如何与两个变量的独立性相关。
•解释应用线性变换对两个随机变量之间的协方差和相关性的影响。
•计算两个随机变量加权和的方差。
•计算二元随机变量组成部分的条件期望。
•描述独立同分布（iid）随机变量序列的特征。
•解释iid属性如何有助于计算iid随机变量总和的均值和方差。
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