10. Annie and Alvie have agreed to meet between 5:00 p.m. and 6:00 p.m. for dinner at a local healthfood restaurant. Let XAnnie s arrival time and Y

Alvie s arrival time. Suppose X and Y are independent with each uniformly distributed on the interval

[5, 6].

a. What is the joint pdf of X and Y ?

b. What is the probability that they both arrive between 5:15 and 5:45?

c. If the rst one to arrive will wait only 10 min before leaving to eat elsewhere, what is the probability that they have dinner at the healthfood restaurant? [Hint: The event of interest is