Question

Please do #13

10 answer is D

11 answer is A

12 answer is A

Please do #13 The options for # 13 is

a) .1482
b) .1696
c) .2134
d) .2387
e) .2516

Thank you

10) Machine "A" has 3 components with independent exponential lifetimes means2, 3 & 5 years). The machine functions if & only if all 3 components function. Determine the probability that the machine functions for more than 5 years, given that it has functioned for more than 2 years. a).079 b) .068 c).056 d) .045 e) .032 11) Continuing (10), machine "B" has 2 components with independent exponential lifetimes (means 5 & 7 years). This machine operates if & only if both components function. Determine the probability that machine A lasts longer than machine B. a).249 b) .282 c) .312 d) .348 e).392 12) Continuing (10), determine the probability that, in Machine A, the component with the lowest expected lifetime outlasts the component with the highest expected lifetime. a) 2/7 b) 3/8 c) 1/8 d) 3/7 e) 2/9 13) Continuing (10), determine the probability that, in machine A, the component with the lowest expected lifetime outlasts both of the other components a) 5/17 b) 12/25 ) 16/31 d) 17/25 e) 11/31

Answer 1

13)for f(X,y,z)=f(x)*f(y)*f(z)=(1/30)*e^-x/2-y/3-z/5

here P(X>(Y,Z)) =P(X>Y>Z)+P(X>Z>Y) =$\int_{0}^{\infty }$$\int_{0}^{x }$$\int_{y}^{z }$ f(x)*f(y)*f(Z) dx dy dz+$\int_{0}^{\infty }$$\int_{0}^{x }$$\int_{z}^{y }$ f(x)*f(y)*f(Z) dx dy dz

=0.1696

option B is correct