Question 9

9. [l9.61 Points] DEVORESTATS 5.1.019. Each front tire on a particular type of vehicle is supposed to be lled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variableX for the right tire and onr the left tire, with joint pdf x\"): K(X2+y2) 205x530,205ys30 0 otherwise (a) Determine the conditional pdf of Ygiven that X = x. fY|X(y|x) = for 20 S y S 30 Determine the conditional pdf ofXgiven that Y = y. fXMXIy) = for 20 s x s 30 3 (b) If the pressure in the right tire is found to be 22 psi, what is the probability that the left tire has a pressure of at least 25 psi? (It is known that K = 380 000 . Round your answer to three decimal places.) : Compare this to P(Y 2 25). (Round your answer to three decimal places.) P(Y 2 25) = (c) If the pressure in the right tire is found to be 22 psi, what is the expected pressure in the left tire, and what is the standard deviation of pressure in this tire? (It is known that 3 K = 380,000 expected pressure psi . Round your answers to two decimal places.) standard deviation psi