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 = 0 and B = 5, then it can be shown that the total waiting time Y has the pdf below . oy 10 (a) Sketch a graph of the pdf of Y. f(y) f(y) f(y) f(y) 0.20 0.20 0.20 0.20 0.15 0.15 0.15 0.15 0.10 0.10 0.10 0.10 0.05 0.05 0.05 0.05 O 2 10 O 2 8 10 O 2 8 10 O 2 6 8 10 (b) Verify that / F(y ) dy = 1. 115 + 10 (c) What is the probability that total waiting time is at most 2 min? (d) What is the probability that total waiting time is at most 9 min? (e) What is the probability that total waiting time is between 2 and 9 min? (f) What is the probability that total waiting time is either less than 1 min or more than 6 min