20. Consider the pdf for total waiting time Y for two buses

2 1

5

 y 0  y  5 f(y)


2 5

  2 1

5

 y 5  y  10 0 otherwise 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]?