Two classes of customers arrive at Paul’s barber shop: class 1 and class 2. Class 1 customers arrive according to a Poisson process with rate λ 1 customers per hour, and class 2 customers arrive...

Two classes of customers arrive at Paul’s barber shop: class 1 and class 2. Class 1 customers arrive according to a Poisson process with rate λ₁
customers per hour, and class 2 customers arrive according to a Poisson process with rate λ₂
customers per hour.

a. What is the probability that no customer arrives over a two-hour period?

b. What is the mean time between customer arrivals at Paul’s shop?

c. Given that a customer has just arrived at the shop, what is the probability that the next customer to arrive at the shop is a class 2 customer?