3. (15 marks) Please write down the probability mass function of the discrete distribution having the following moment generating function: M(t) = (5/12)e' + (1/3)e-2 +(1/4)est. Please also find the mean and variance of the distribution. 4. (10 marks) Let X be a Poisson random variable with parameter 2. Show that P(X=k) increases monotonically and then decreases monotonically as k increases, attaining its maximum when k is the largest integer not exceeding 2. 5. (12 marks) Consider a biased coin that when flipped comes up heads with probability 0.6. The coin is flipped until either heads or tails has occurred three times. Find the expected number of flips