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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(x, y) = {K JK(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 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 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 JK(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 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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(c) Give a word description of the event { X0 and Y = 0). One hose is in use on one island. At least one hose is in use at both islands. One hose is in use on both islands. At most one hose is in use at both islands. Compute the probability of this event. P(X = 0 and Y = 0) = [ (d) Compute the marginal pmf of X. y ox(x) Compute the marginal pmf of Y. Py(x) 0 P(X ≤ 1) = 0 1 1 Using Px(x), what is P(X ≤ 1)? 2 2 (e) Are X and Y independent rv's? Explain. Ox and Y are independent because P(x, y) = Px(x) · Py(y). OX and Y are not independent because P(x, y) +Px(x) · Py(y). Ox and Y are not independent because P(x, y) = Px(x) · Py(y). OX and Y are independent because P(x, y) = Px(x) - PY(y).
Transcribed Image Text:(c) Give a word description of the event { X0 and Y = 0). One hose is in use on one island. At least one hose is in use at both islands. One hose is in use on both islands. At most one hose is in use at both islands. Compute the probability of this event. P(X = 0 and Y = 0) = [ (d) Compute the marginal pmf of X. y ox(x) Compute the marginal pmf of Y. Py(x) 0 P(X ≤ 1) = 0 1 1 Using Px(x), what is P(X ≤ 1)? 2 2 (e) Are X and Y independent rv's? Explain. Ox and Y are independent because P(x, y) = Px(x) · Py(y). OX and Y are not independent because P(x, y) +Px(x) · Py(y). Ox and Y are not independent because P(x, y) = Px(x) · Py(y). OX and Y are independent because P(x, y) = Px(x) - PY(y).
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(x, y) = JK(r² + y²) 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.) (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(x, y) = fx(z) fy(y), so X and Y are not independent. ONO, f(x, y) + fx(2) fy(y), 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(x, y) = JK(r² + y²) 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.) (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(x, y) = fx(z) fy(y), so X and Y are not independent. ONO, f(x, y) + fx(2) fy(y), so X and Y are not independent.
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