1. Philip throws a fair die until he obtains a four. Diane then tosses a coin as many times as Philip threw his die. Determine the expected value and variance of the number of

(a) heads,

(b) tails, and

(c) heads and tails obtained by Diane.

2. Let p be the probability that the tip points downward after a person throws a drawing pin once. Miriam throws a drawing pin until it points downward for the first time. Let X be the number of throws for this to happen. She then throws the drawing pin another X times. Let Y be the number of times the drawing pin points downward in the latter series of throws. Find the distribution of Y (cf. Problem 2.6.38).