24. Consider the pdf for total waiting time Y for two buses introduced in Exercise 8.

a. Compute and sketch the cdf of Y. [Hint: Consider separately 0 y  5 and 5 y

10 in computing F(y). A graph of the pdf should be helpful.]

b. Obtain an expression for the (100p)th percentile.

(Hint: Consider separately 0  p  .5 and .5 

p  1.)

c. Compute E(Y) and V(Y). How do these compare with the expected waiting time and variance for a single bus when the time is uniformly distributed on [0, 5]?

d. Explain how symmetry can be used to obtain E(Y).