111. After shuf ing a deck of 52 cards, a dealer deals out 5. Let X  the number of suits represented in the ve-card hand.

a. Show that the pmf of X is x 1 2 3 4 p(x) .002 .146 .588 .264

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

b. Compute m, s2, and s.