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Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: -x(1 + y) x 2 0 and y 2 0 f(x, y) = otherwise (a) What is the probability that the lifetime X of the first component exceeds 3? (Round your answer to three decimal places.) (b) What is the marginal pdf of X? xe-x(1+y)dx = eY for y 2 0 xe-x(1+y)dy = e-X for x 2 0 ve-x(1+y)dx = e=X for x 2 0 xe-x(1+y)dx = 1 for y 2 0 (1 + y)2 1 xe-x(1+y)dx = for x 2 0 (1 + x)2 ye-y(1+x)dy = eY for y > 0 What is the marginal pdf of Y? 1 ye-Y(1+x)dx for x 2 0 (1 + x)2 xe-X(1+y)dx = 1 for y 2 0 (1 + y)2 1 O ve-y(1+x)dx = for x 2 0

Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: -x(1 + y) x 2 0 and y 2 0 f(x, y) = otherwise (a) What is the probability that the lifetime X of the first component exceeds 3? (Round your answer to three decimal places.) (b) What is the marginal pdf of X? xe-x(1+y)dx = eY for y 2 0 xe-x(1+y)dy = e-X for x 2 0 ve-x(1+y)dx = e=X for x 2 0 xe-x(1+y)dx = 1 for y 2 0 (1 + y)2 1 xe-x(1+y)dx = for x 2 0 (1 + x)2 ye-y(1+x)dy = eY for y > 0 What is the marginal pdf of Y? 1 ye-Y(1+x)dx for x 2 0 (1 + x)2 xe-X(1+y)dx = 1 for y 2 0 (1 + y)2 1 O ve-y(1+x)dx = for x 2 0

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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Are the two lifetimes independent? Explain. Yes, f(x, y) is the product of the marginal pdfs. The two lifetimes are independent. Yes, f(x, y) is not the product of the marginal pdfs. The two lifetimes are independent. No, f(x, y) is the product of the marginal pdfs. The two lifetimes are not independent. No, f(x, y) is not the product of the marginal pdfs. The two lifetimes are not independent. (c) What is the probability that the lifetime of at least one component exceeds 3? (Do not round intermediate values. Round your answer to three decimal places.)
Transcribed Image Text:Are the two lifetimes independent? Explain. Yes, f(x, y) is the product of the marginal pdfs. The two lifetimes are independent. Yes, f(x, y) is not the product of the marginal pdfs. The two lifetimes are independent. No, f(x, y) is the product of the marginal pdfs. The two lifetimes are not independent. No, f(x, y) is not the product of the marginal pdfs. The two lifetimes are not independent. (c) What is the probability that the lifetime of at least one component exceeds 3? (Do not round intermediate values. Round your answer to three decimal places.)
Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: Sxe-x(1 + y) x > 0 and y > 0 f(x, у) %3D otherwise (a) What is the probability that the lifetime X of the first component exceeds 3? (Round your answer to three decimal places.) (b) What is the marginal pdf of X? xe-X(1+y)dx = e¯Y for y > 0 xe-x(1+y)dy = e -X for x > 0 00 ,-x(1+y)dx = e¯X for x > 0 ye xe-X(1+y)dx = for y 2 0 (1 + y)2 00 1 xe-x(1+y)dx = for x 2 0 (1 + x)2 To ye-Y(1+x)dy = e=Y for y > 0 What is the marginal pdf of Y? 1 ye¬Y(1+x)dx for x 2 0 (1 + x)² 00 1 -x(1+y)dx for y 2 0 хе (1 + y)² 1 ye-Y(1+x)dx for x 2 0 (1 + y)² xe-x(1+y)dx = for y 2 0 (1 + x)2 ve-x(1+y)dx = e¯Y for y > 0 xe-X(1+y)dy = e¯X for x > 0
Transcribed Image Text:Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: Sxe-x(1 + y) x > 0 and y > 0 f(x, у) %3D otherwise (a) What is the probability that the lifetime X of the first component exceeds 3? (Round your answer to three decimal places.) (b) What is the marginal pdf of X? xe-X(1+y)dx = e¯Y for y > 0 xe-x(1+y)dy = e -X for x > 0 00 ,-x(1+y)dx = e¯X for x > 0 ye xe-X(1+y)dx = for y 2 0 (1 + y)2 00 1 xe-x(1+y)dx = for x 2 0 (1 + x)2 To ye-Y(1+x)dy = e=Y for y > 0 What is the marginal pdf of Y? 1 ye¬Y(1+x)dx for x 2 0 (1 + x)² 00 1 -x(1+y)dx for y 2 0 хе (1 + y)² 1 ye-Y(1+x)dx for x 2 0 (1 + y)² xe-x(1+y)dx = for y 2 0 (1 + x)2 ve-x(1+y)dx = e¯Y for y > 0 xe-X(1+y)dy = e¯X for x > 0
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