A ferry boat leaves the dock once per hour. Your waiting time for the next ferryboat will follow a uniform distribution from 0 to 60 minutes. a. Find the mean and variance of this random variable.
b. Find the probability of waiting more than 20 minutes for the next ferry.
c. Find the probability of waiting exactly 20 minutes for the next ferry.
d. Find the probability of waiting between 15 and 35 minutes for the next ferry.
e. Find the conditional probability of waiting at least 10 more minutes after you have already waited 15 minutes.
f. Find the probability of waiting more than 45 minutes for the ferry on 3 consecutive independent days.