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ch 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(x, y): 1) = {K(x² + √²) 20 ≤ x ≤ 30, 20 ≤ y ≤ 30 otherwise 0 (a) Determine the conditional pdf of Y given that Xx. fylx(xx) = for 20 sy s 30 Determine the conditional pdf of X given that Y= y. fx|x(xly) = for 20 ≤ x ≤ 30 (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 ≥ 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 the standard deviation of pressure in this tire? (It is known that K = 3 Round your answers 380,000 expected pressure psi psi standard deviation two decimal places.)

ch 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(x, y): 1) = {K(x² + √²) 20 ≤ x ≤ 30, 20 ≤ y ≤ 30 otherwise 0 (a) Determine the conditional pdf of Y given that Xx. fylx(xx) = for 20 sy s 30 Determine the conditional pdf of X given that Y= y. fx|x(xly) = for 20 ≤ x ≤ 30 (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 ≥ 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 the standard deviation of pressure in this tire? (It is known that K = 3 Round your answers 380,000 expected pressure psi psi standard deviation two 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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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 [K(x² + y²) 20 ≤ x ≤ 30, 20 ≤ y ≤ 30 = f(x, y) = otherwise (a) Determine the conditional pdf of Y given that X = x. fy|x(y|x) = for 20 ≤ y ≤ 30 Determine the conditional pdf of X given that Y = y. fx|x(xly) = for 20 ≤ x ≤ 30 Round your answer to three decimal places.) (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 Compare this to P(Y≥ 25). (Round your answer to three decimal places.) P(Y ≥ 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 K = 380,000 expected pressure psi psi standard deviation Round your answers to two decimal places.)
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 [K(x² + y²) 20 ≤ x ≤ 30, 20 ≤ y ≤ 30 = f(x, y) = otherwise (a) Determine the conditional pdf of Y given that X = x. fy|x(y|x) = for 20 ≤ y ≤ 30 Determine the conditional pdf of X given that Y = y. fx|x(xly) = for 20 ≤ x ≤ 30 Round your answer to three decimal places.) (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 Compare this to P(Y≥ 25). (Round your answer to three decimal places.) P(Y ≥ 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 K = 380,000 expected pressure psi psi standard deviation Round your answers to two decimal places.)
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