(solution) Leon leaves his office every day at a random time between 4:30 P.M. and 5:00 P.M. If he leaves t…

(solution) Leon leaves his office every day at a random time between 4:30 P.M. and 5:00 P.M. If he leaves t…

Leon leaves his office every day at a random time between 4:30 P.M. and 5:00 P.M. If he leaves t minutes past 4:30, the time it will take him to reach home is a random number between 20 and 20 + (2t)/3 minutes. Let Y be the number of minutes past 4:30 that Leon leaves his office tomorrow and X be the number of minutes it takes him to reach home. Find the joint probability density function of X and Y.