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Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose actual air pressure in each tire is a random variable, X for the right tire and Y for the left tire, with joint pdf f(x, y) = {K K(z² + y²) 20≤x≤30, 20 ≤ y ≤ 30 otherwise (a) What is the value of K? (Enter your answer as a fraction.) (b) What is the probability that both tires are underfilled? (Round your answer to four decimal places.) (c) What is the probability that the difference air pressure between the two tires is at most 2 psi? (Round your answer to four decimal places.)

Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose actual air pressure in each tire is a random variable, X for the right tire and Y for the left tire, with joint pdf f(x, y) = {K K(z² + y²) 20≤x≤30, 20 ≤ y ≤ 30 otherwise (a) What is the value of K? (Enter your answer as a fraction.) (b) What is the probability that both tires are underfilled? (Round your answer to four decimal places.) (c) What is the probability that the difference air pressure between the two tires is at most 2 psi? (Round your answer to four decimal places.)

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable, X for the right tire and Y for the left tire, with joint pdf f(z,y) = { K (2³² + (x² + y²) 20 ≤ ≤ 30, 20 ≤ y ≤ 30 otherwise (a) What is the value of K? (Enter your answer as a fraction.) K=|| (b) What is the probability that both tires are underfilled? (Round your answer to four decimal places.) (c) What is the probability that the difference in air pressure between the two tires is at most 2 psi? (Round your answer to four decimal places.) (d) Determine the (marginal) distribution of air pressure in the right tire alone. for 20 < x < 30 (e) Are X and Y independent rv's? Oves, f(x, y) = fx(z) - fy (y), so X and Y are independent. Oves, f(z,y) #fx(z) - fy (y), so X and Y are independent. ONO, f(x, y) = fx(z) - fy(y), so X and Y are not independent. ONO, f(x, y) + fx(z) - fy(u), so X and Y are not independent.
Transcribed Image Text:Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable, X for the right tire and Y for the left tire, with joint pdf f(z,y) = { K (2³² + (x² + y²) 20 ≤ ≤ 30, 20 ≤ y ≤ 30 otherwise (a) What is the value of K? (Enter your answer as a fraction.) K=|| (b) What is the probability that both tires are underfilled? (Round your answer to four decimal places.) (c) What is the probability that the difference in air pressure between the two tires is at most 2 psi? (Round your answer to four decimal places.) (d) Determine the (marginal) distribution of air pressure in the right tire alone. for 20 < x < 30 (e) Are X and Y independent rv's? Oves, f(x, y) = fx(z) - fy (y), so X and Y are independent. Oves, f(z,y) #fx(z) - fy (y), so X and Y are independent. ONO, f(x, y) = fx(z) - fy(y), so X and Y are not independent. ONO, f(x, y) + fx(z) - fy(u), so X and Y are not independent.
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