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...

Extracted 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.)


Extracted 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