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Question 2: Jointly distributed random variables (40 points) Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 24 psi. Suppose the actual air pressure in each tire is a random variable: X for the left tire and Y for the right tire, with joint pdf K(+2) 20 $ $ 30,20 5 5 30 otherwise 0 a) Show that K 380 000 110 points) b) What is the probability that both tires are underfilled? 110 points) c) Determine the (marginal) distribution of air pressure in the right tire alone. [10 points d) Are X and Y independent random variables? (10 points