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stock_watson_ch2_3 - Stock and Watson Chapter 2.3 Two...

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Stock and Watson Chapter 2.3- Two Random Variables Joint distribution The joint probability distribution of two discrete random variables, say X and Y , is the probability that the random variables simultaneously take on certain values, say x and y . The probabilities of all possible ( x , y ) combinations sum to 1. The joint probability distribution can be written as the function Pr( X = x , Y = y ). Rain ( X =0) No Rain ( X =1) Total Long Commute ( Y =0) 0.15 0.07 0.22 Short Commute ( Y =1) 0.15 0.63 0.78 Total 0.30 0.70 1.00 Pr( X =0, Y =0) = Pr( X =0, Y =1) = Pr( X =1, Y =0) = Pr( X =1, Y =1) = Marginal distribution The marginal probability distribution of a random variable Y is just another name for its probability distribution. This term is used to distinguish the distribution of Y alone (the marginal distribution) from the joint distribution of Y and another random variable. The marginal distribution of Y can be computed from the joint distribution of X and Y by adding up the probabilities of all possible outcomes for which Y takes on a specified value. If X
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