39. Choose a number X at random from the set of numbers (1, 2, 3, 4, 5)....

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39. Choose a number X at random from the set of numbers (1, 2, 3, 4, 5). Now choose a number at random from the subset no larger than X, that is, from (1,..., X). Call this second number Y.

(a) Find the joint mass function of X and Y.

(b) Find the conditional mass function of X given that Y = i. Do it for i = 1, 2, 3, 4, 5.

(c) Are X and Y independent? Why?

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