In commuting to work, a professor must first get on a bus near her house and then transf...

In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with A = 0and B = 0 , 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?