The Lower Bay State Road neighborhood is organizing an egg hunt and a Bostonian brunch at Easter. Both community events start at noon. Let X be the duration of the egg hunt in minutes, and Y be the duration of the brunch in minutes. Let FX be the CDF of X, and FY be the CDF of Y . Finally, suppose X and Y are independent.
Student organizer Asami stays from noon until both events are over. Let Z be the length of time
she stays in minutes. For example, if X = 50 and Y = 40, then Z = 50.
(a) Express Pr(Z ≤ 30) in terms of FX and FY .
Resident assistant Charlotte only stays from noon until either event is over. Let W be the length
of time she stays in minutes. For example, if X = 50 and Y = 40, then W = 40.
(b) Express Pr(W ≤ 30) in terms of FX and FY .