A student waits for a bus. Let X be the number of hours that the student waits. Assume that the waiting time is Exponential with average 20 minutes.
a. What is the probability that the student waits more than 30 minutes?
b. What is the probability that the student waits more than 45 minutes (total), given that she has already waited for 20 minutes?
c. Given that someone waits less than 45 minutes, what is the probability that they waited less than 20 minutes?
d. What is the standard deviation of the student's waiting time?