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

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

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]?

Reference exercise 8

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

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?