8. Commuting to work requires getting on a bus near home and then transferring to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with A  0 and B  5, then it can be shown that the total waiting time Y has the pdf

a. Sketch a graph of the pdf of Y.

b. Verify that .

c. What is the probability that total waiting time is at most 3 min?

d. What is the probability that total waiting time is at most 8 min?

e. What is the probability that total waiting time is between 3 and 8 min?

f. What is the probability that total waiting time is either less than 2 min or more than 6 min?