Question 2. (15 MARKS] Suppose you have three coins. Coin A has a probability of heads of 0.75, Coin B has a probability of heads of 0.5, and Coin C has a probability of heads of 0.25. (a) [5 MARKS] Suppose you flip all three coins at once, and let X be the number of heads you see (which will be between 0 and 3). What is the expected value of X, E[X]? (b) (10 MARKS] Suppose instead you put all three coins in your pocket, select one at random, and then flip that coin 5 times. You notice that 3 of the 5 flips result in heads while the other 2 are tails. What is the probability that you chose Coin C? Hint: Define random variable D as the observed data, and notice that you can compute p(D = 3 heads and 2 tails|Coin = C)