Fred and Gretchen are waiting at a bus stop in Blotchville. Two bus routes, Route 1 and Route 2, have buses that stop at this bus stop. For Route i, buses arrive according to a Poisson process with...

Fred and Gretchen are waiting at a bus stop in Blotchville. Two bus routes, Route 1 and Route 2, have buses that stop at this bus stop. For Route i, buses arrive according to a Poisson process with rate Ai buses/minute. The Route 1 process is independent of the Route 2 process. Fred is waiting for a Route 1 bus, and Gretchen is waiting for a Route 2 bus. (a) Given that Fred has already waited for 20 minutes, on average how much longer will he have to wait for his bus? (b) Find the probability that at least it Route 1 buses will pass by before the first Route 2 bus arrives. The following result from Chapter 7 may be useful here: for independent random variables X1 Expo(A1), X2 r- Expo(A2), we have P(Xi.