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JK(x² + y²) f(x, y) = 0 20≤x≤ 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.)

JK(x² + y²) f(x, y) = 0 20≤x≤ 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.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Help with Symbolic Notation 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(x, y) = {K(2 JK(x² + y²) 20 ≤ x ≤ 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? OYes, f(x, y) = fx(x) · fy(y), so X and Y are independent. OYes, f(x,y) ‡ £x(x) · fy(y), so X and Y are independent. ONO, f(x, 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:Help with Symbolic Notation 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(x, y) = {K(2 JK(x² + y²) 20 ≤ x ≤ 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? OYes, f(x, y) = fx(x) · fy(y), so X and Y are independent. OYes, f(x,y) ‡ £x(x) · fy(y), so X and Y are independent. ONO, f(x, 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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