Problem 2 We consider a random selection of coins, Where the probability of heads, C for the coins is a random variable Whose pdf is fc(c) = k - c for 0 S c S 1 and zero otherwise. (a) Find 13. (b) Find P(H) for a single coin toss. (c) Let E be the event that we choose a coin, ip it n times, and heads appears k: of these times. Find P(E). (d) Find the conditional pdf fC|E(c|E). (e) Find the probability that heads appears in the (n + 1)st toss given that k heads has appeared in the rst n tosses