Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: 0 f(x, y ) = xe-x(1 + >) x 20 andy 20 otherwise 0498 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? ve - * ( ity ) dx = e - * for x 20 ( xe - x ( ity )dy = e- * for x 20 xe - x ( ity )dx = e- y for y zo xe -x(1+y)dx =. 1 ( 1 + y ) 2 for y 2 0 O Jo xe - x(1+y)dx = 1 (1+ * ) 2 7 for x 2 0 ( ye- y(itx)dy = e- Y for y 20 X What is the marginal pdf of y? ove - * ( ity ) d* = e - y for y zo ( xe - x( ity)dy = e-* for x 20 yev(1+x ) dx = (1+ *) 2 for x 2 0 ye y(1+x)dx = 1 ( 1+ y )2 for x 2 xe - x (1+y)dx = 1 ( 1 + y ) 2 for y 2 0 xe -x(1+y)dx = - 1 (1 + x) 2 for y 2 0Are the two lifetimes independent? Explain. 0 Yes, x, y) is the product of the marginal pdfs. The two lifetimes are independent. 0 Yes, x, y) is not the product of the marginal pdfs. The two lifetimes are independent. 6) No, x, 1;) is the product of the marginal pdfs. The two lifetimes are not independent. 0 No, x, 1;) is not the product of the marginal pdfs. The two lifetimes are not independent. X (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.) Ex