Please solve with steps

(4) Solve the following problems. (a) [3pts] You are walking on the street. The number of people you see in a minute follows Poiss0n(2) distribution. Let's say X is the number of people you see in an hour. What is the distribution of X '? What is the probability that you see more than 10 people? (That is, 11, 12, 13,...) (b) [2pts] (This problem shares a similar concept with Q2 in HW4.) Let f be the probability mass function of PoissonOs). That is, f (11?) = e'Akm/asl for a: = 0, 1, 2, First, solve the inequality at) 2 at 1). Then, show that f(:L') is maximized at :1: = [A]. Once again, [A] means the largest integer which is less than or equal to A