RANDOM VARIABLES AND DISTRIBUTIONS

Discrete probability distribution: Word problems

Suppose that the genders of the three children of a certain family are soon to be revealed . Outcomes are thus triples of " girls " ( 8 ) and " boys " ( 5 ) , which we write &b 8 , b bb , etc . For each outcome , let & be the random variable counting the number of girls in each outcome . For example , if the outcome is 8 68 , then* R ( 868 ) = 2. Suppose that the random variable* is defined in terms of & as follows : * = 2 R - 4 R - 3 . The values of* are thus :` \\Outcome\\ 8 88\\ 8 8 6| 8 6 8\\b b b| 8 b b|3 8 6\\6 6 8|6 8 8 `*\\ 3\\ - 3\\ - 3\\ - 3\\ - 5\\ - 5\\ - 5\\ - 3| Calculate the probability distribution function of I , i.e . the function !* ( *