HW5

Dear all,

Here is HW5.

1. Let X1 and X2 be two discrete random variables whose outcomes do not overlap. And let X=X1 with prob p and X=X2 with prob (1-p). Show that

H(X) = p H(X1) + (1-p) H(X2) + H(p)

2. Consider Teams A and B play against each other for the final of a volleyball tournament. The team who won 3 matches first win the tournament. Let X be the outcome of the game. For example, X can be AAA, BBB, AABA, ABAA. And let Y be the number of matches played, so Y can be 3,4, or 5. Please try to compute a) H(X) b) H(Y) c) H(X|Y) d) H(Y|X) e) H(X,Y)

Best,

Sam