(a) [3pts] You are walking on the street. The number of people you see in a minute follows Poisson(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 Poisson().

That is, f(x) = e^()^(x)/x! for x = 0, 1, 2, . First, solve the inequality f(x) f(x 1). Then, show that f(x) is maximized at x = . Once again, means the largest integer which is less than or equal to .