9. Checking emails. Caroline has a busy email: New messages arrive with rate A = 9 per hour, and she checks her email with rate A = 1 per hour, independent of email arrivals. Suppose both processes (emails arriving and Caroline checking her email) are Poisson arrival processes. (a) (4 pts) What is the chance she gets 5 new messages and she checks her email twice in an hour? (b) (3 pts) Thinking of this total Poisson process (with rate 10 per hour) as a superposition of two thinned Poisson processes (new arrivals and checking email), what is the probability an arrival is a new message and what is the probability an arrival is Caroline checking her email? (c) (3 pts) What is the distribution of the number of new messages she will see each time she checks her email