Suppose that you are waiting for a friend to call you andthat the time you wait in minutes has an exponential distribution with parameter λ = 0

Suppose that you are waiting for a friend to call you andthat the time you wait in minutes has an exponential distribution with parameter λ = 0.1.

(a) What is the expectation of your waiting time?

(b) What is the probability that you will wait longer than

10 minutes?(c) What is the probability that you will wait less than

5 minutes?

(d) Suppose that after 5 minutes you are still waiting for

the call. What is the distribution of your additional

waiting time? In this case, what is the probability that

your total waiting time is longer than 15 minutes?

(e) Suppose now that the time you wait in minutes for

the call has a U(0, 20) distribution. What is the

expectation of your waiting time? If after 5 minutes

you are still waiting for the call, what is the

distribution of your additional waiting time?