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Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 25 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 (z² + y²) 20 ≤ ≤ 30, 20 ≤ y ≤ 30 otherwise

Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 25 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 (z² + y²) 20 ≤ ≤ 30, 20 ≤ y ≤ 30 otherwise

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 1CR
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Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 25 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 (z² + y²) 20≤x≤ 30, 20 ≤ y ≤ 30 otherwise
Transcribed Image Text:Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 25 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 (z² + y²) 20≤x≤ 30, 20 ≤ y ≤ 30 otherwise
(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? OYes, f(x, y) = fx(z) - fy(y), so X and Y are independent. OYes, f(x, y) + fx(x) fy(y), so X and Y are independent. ONO, f(z,y) = fx(x) · fy(y), so X and Y are not independent. ONO, f(x, y) + fx(x) fy(y), so X and Y are not independent.
Transcribed Image Text:(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? OYes, f(x, y) = fx(z) - fy(y), so X and Y are independent. OYes, f(x, y) + fx(x) fy(y), so X and Y are independent. ONO, f(z,y) = fx(x) · fy(y), so X and Y are not independent. ONO, f(x, y) + fx(x) fy(y), so X and Y are not independent.
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