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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 1 = {K(x² + y²) 0 f(x, y) = 20 ≤ x ≤ 30, 20 ≤ y ≤ 30 otherwise

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 1 = {K(x² + y²) 0 f(x, y) = 20 ≤ x ≤ 30, 20 ≤ y ≤ 30 otherwise

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 + y²) = {K(x²+ 20 ≤ x ≤ 30, 20 ≤ y ≤ 30 otherwise (a) Determine the conditional pdf of Y given that X = x. fXlX(XIX) for 20 ≤ y ≤ 30 f(x, y) = Determine the conditional pdf of X given that Y = y. FX₁Y(XY): = 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 3 25 psi? (It is known that K = Round your answer to three decimal places.) 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 3 standard deviation of pressure in this tire? (It is known that K = Round your answers to two decimal places.) 380,000 expected pressure standard deviation psi psi
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 + y²) = {K(x²+ 20 ≤ x ≤ 30, 20 ≤ y ≤ 30 otherwise (a) Determine the conditional pdf of Y given that X = x. fXlX(XIX) for 20 ≤ y ≤ 30 f(x, y) = Determine the conditional pdf of X given that Y = y. FX₁Y(XY): = 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 3 25 psi? (It is known that K = Round your answer to three decimal places.) 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 3 standard deviation of pressure in this tire? (It is known that K = Round your answers to two decimal places.) 380,000 expected pressure standard deviation psi psi
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