Bob is waiting for his girlfriend Alice to call. His waiting time X is exponentially distributed, with expected waiting time K(X) = 0.20 hours, i.e., 12 minutes.
a. What is the probability that he must wait more than 12 minutes for her to call?
b. What is the probability that he must wait more than 12 minutes (altogether) for her to call, given that he has already waited 3 minutes?
c. What is the probability that he must wait at most 10 minutes (altogether) for her to call, given that he has already waited 3 minutes?
d. Given that he waited less than 10 minutes, what is the probability that he waited less than 3 minutes?
e. Find the unique time "a" in hours such that P(X ≤ a) = 1/2 and
P(X > a) = 1/2. This is the median waiting time; also see Exercise 32.13.