(Total: 16 points) The number of deals made by an agent on a given day is modelled by a non-negative integer-valued random variable X. The k-th moment of X is given by E(Xk)=63+2k+1,fork{1,2,3,} (a) (3 points) Find the mean and variance of the number of deals. (b) (3 points) Show that for any positive integer k, Pr(X3)21(31)k+31(32)k [Hint: Consider Markov's inequality.] (c) (2 points) Show that it is impossible for the agent to make more than 2 deals per day. (d) (3 points) Using the result of part (c), determine the probability mass function of X. (e) (5 points) Without using the result of part (d), find the moment generating function of X