1. A soccer player is attempting a penalty kick. Let the joint distribution of Where the kick is targeted be given by 190331): 0(5) i ITIXIO i h)? T E (*5: 5):h E (0310) Where R represents the horizontal distance right of center [in yards) and H represents the vertical distance (in feet). a. Are R and H independent? b. Find 0 that makes this a valid joint density. Hint: the density is symmetric about R = 0, so it is easier [110'le h) (2 [05(5) TM?) dh e. Let G be a random variable that equals 1 if a goal is scored and 0 if a save is made. The conditional to evaluate: probability of a goal is given by p(G : 1|r, h) : (1/32)? + [1/16)h, |r|