Suppose you keep ipping a coin until you observe 3 heads. The random variable X is the number of ips that is required. Based on the observation, you need to choose one of the following two hypothesis: H0: it is a fair coin with P(H) : 0.5, and H1: the coin is bent with P(H) : g. (a) Describe the ML decision rule. Express it in a simplied form. (Hint: 1(1):: 2 5.13.) (b) Describe the MAP decision rule under the assumption that H0 is a priori twice as likely as H1. Express it in a simplied form. (Hint: 113511.65 : 6.84.) (c) Find the average error probability, pa, for the ML rule. (d) Find the average error probability, pa, for the MAP rule, using the same prior distribution given in part (b)