Suppose that the monorail from Newark Liberty Airport to New York City leaves every hour. Let X be the random variable that represents the time in minutes a person arriving at the monorail terminal at a random time must wait until the next train leaves. Assume X has a uniform distribution.

a. Find the probability density function for X.

b. Find the probability that a person has to wait at least 45 minutes for the next train to New York.

c. Find the probability that a person has to wait between 5 and 15 minutes for the next train.