Consider the pdf for total waiting time Y? ? or 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 (100?p?)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.?? ketch a graph of the pdf of ?Y?. b.?? erify that . c.?? hat is the probability that total waiting time is at most 3 min? d.?? hat is the probability that total waiting time is at most 8 min? e.?? hat 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?

Answer Step 1 of 3 a)For 0y<5 y 1 1 2 y f(y)= 25y dy= 50 [ ] 0 0 1 2 = 50y