2. (Joint Probability Distribution, Continuous Random Variable) Annie and Alvie have agreed to meet for lunch between noon (0:00 PM.) and 1:00 PM at a local healthfood restaurant. Denote Annie's arrival time by X , Alvie's by Y, and suppose X and Y are independent with pdf's 39:2 059251, 0 otherwise. fXCSE) = { 2y 0 s y s 1, :1: = fY( ) {U otherwise. (a) (3 points) \"at is the joint pdf of X and Y? (b) (3 points) \"at is the probability that they both arrive between 0:15 PM. and 0:45 P.M.? (c) [4 points) 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? That is, P(|X Y| g i). (d) [2 points (bonus)) What is the expected amount of time that the one who arrives rst must wait for the other person? That is EHX Y|]