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Chapter 4 Joint Distributions Xuerong Meggie Wen Missouri University of Science and Technology Chapter 4 Joint Distributions - p. 1/133
Joint Discrete Distributions It is often of interest to consider probabilities for more than one random variable at a time. For example, X 1 is the height of a man (inches), X 2 is the height of his son (inches), we are interested in P ( X 2 60 | 60 X 1 61) . Definition 1. A k -dimensional random vector is a function from S (sample space) to R k . We may denote it as X = ( X 1 , . . . , X k ) , where X i s are a random variables; or ( X, Y, Z, . . . ) . Chapter 4 Joint Distributions - p. 2/133
Example 1. Toss two regular dice. Let X = maximum dot , Y = abolute difference , Z = sum of two dice , then ( X, Y, Z ) is a three-dimensional random vector. Definition 2. Let ( X, Y ) be discrete random vector, then the function p ( x, y ) = P ( X = x, Y = y ) is called the joint probablity mass function. Chapter 4 Joint Distributions - p. 3/133
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