Question 32 Two people agree to meet for a drink after work

Question #32

Two people agree to meet for a drink after work but they are impatient and each will wait only 15 minutes for the other person to show up. Suppose that they each arrive at independent random times uniformly distributed between 5 P.M. and 6 P.M. What is the probability they will meet? Suppose X is uniform on (0, 1) and Y = X. Find the joint distribution function of X and Y. A pair of random variables X and Y takes values between 0 and has P(X x, Y y) = x3y2 when 0 x, y 1. Find the joint density function.

Solution