The problem of passenger congestion prompted a large international airport to install a monorail connecting its main terminal to the three concourses, A, B, and C. The engineers designed the monorail so that the amount of time a passenger at concourse B must wait for a monorail car has a uniform distribution ranging from 0 to 10 minutes.

a. Find the mean and variance of Y, the time a passenger at concourse B must wait for the monorail. (Assume that the monorail travels sequentially from concourse A, to concourse B, to concourse C, back to concourse B, and then returns to concourse A. The route is then repeated.)

b. If it takes the monorail 1 minute to go from concourse to concourse, find the probability that a hurried passenger can reach concourse A less than 4 minutes after arriving at the monorail station at concourse B.