(a) Consider a Poisson random variable X with parameters A and T. Let px (k) denote the PMF of X and let k* be the largest integer that is less than or equal to AT. Show that k* = arg maxkerufo) px (k). (Hint: Show that the PMF of X is monotonically non-decreasing with & in the range from 0 to * and is monotonically decreasing with k for k > k*. ) (b) Let X1, X2, ... . Xn be n independent Geometric random variables with the same success probability pe (0, 1). Define X = min(X1, . .., Xn). What is the PMF of X? What kind of random variable is X