95. After shuffling a deck of 52 cards, a dealer deals out 5. Let X the

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95. After shuffling a deck of 52 cards, a dealer deals out 5. Let X  the number of suits represented in the five-card hand.

a. Show that the pmf of X is

[Hint: p(1)  4P(all are spades), p(2)  6P(only spades and hearts with at least one of each suit), and p(4)

 4P(2 spades one of each other suit).]

b. Compute , 2

, and .

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