Problem 1 Scenario: You purchase an iPhone with Apple Care, where you are only allowed to make two claims of damage per year. Suppose X and Y represents the size of the rst and second claim you make. X and Y are discrete random variables that have a joint density function given by: i for a: = 100,200,400; = 200,400,800; :1: 5 rm?!) = {24m y y 0 otherwise Apple Care's policy will cover the rst claim, X and half of the second claim, Y. Find the probability that the total claim amount paid by Apple is at most $500