Joint Distribution of Several Random Variables
Multivariate statistical methods are useful when they offer some advantage over a variable by variable approach. In Example 1.1, we saw that considering one variable at a time may not be optimal for classification purposes. Hence, it is important that we establish some terminology and acquire a basic knowledge of bivariate and multivariate distribution theory. In particular, we shall discuss notions such as independence of random variables, covariance and correlation, marginal and conditional distributions, and linear transformations of random variables. In the spirit of keeping this chapter on an elementary level, we shall restrict ourselves to the case of two variables most of the time, and outline the general case of p ≥ 2 jointly distributed random variables only toward the end in Section 2.10.
KeywordsJoint Distribution Conditional Distribution Marginal Distribution Wing Length Discrete Random Variable
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