Question

Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: FY 1 xe A1 + + x2 0 and v2 0 1 0 otherwise (a) What is the probability that the lifetime X of the first component exceeds 4? (Round your answer to three decimal places.) (b) What is the marginal pdf of X? xe X(1+y)dy = e X for x 2 0 dx = 1 (1 + vi for y xe X(1+y)dx m y for. (1+x1 for xzo *(1+y)dx = e for for x 20 xe X(1+x)dx = en for y2 0 +x)dy - e- for y20

Answer 1

2) - ( ). осч узо heh hex [17, 18 (14х1 ] [x] емесе ер (с)

otarace C Marginal polf of x . f(a) farme dy .= xé - p - 2 - Xe* a ex %. ; deso. () em ; 220-

Marging Marginal pdf of falo)Smerigo (1+) 74 [new year 2011 xe-xlity) - 1+ 2 - folytje; ydo Now, +(a) f(a) lagja en f(,w). u. The 2 lifetines are not in dept. 9) P[x34 Ur>*] 2 P(x>4] +P{{34] - P[*24 2474]. je robe longe dy jſme*( - ay" - * 1 *w) andy 00 dx dy. 44 nelity) andy

Now, 00 xe-xlles) de dredy ce obc.) - 5 Prob. that fetime of at each one component exceeds 45 - : 0.218.