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# Suppose that the two components operate independently and have identical performance characteristics. Let X and Y...

Suppose that the two components operate independently and have identical performance characteristics. Let X and Y be random variables denoting their life spans. Experience with wear-out times suggests that in certain cases a good choice for fx,y(x, y) would be fxx (x, y) = {?? 122e-1(x+y), x > 0,y>0 otherwise Where 2 is some constant greater than 0. Suppose that the manufacturer advertises a money-back guarantee if the system fails to last for more than 1000 hours. a) What proportion of the systems sold is likely to be returned for refunds? b) P(Y < 1000|X > 1000) =? c) E(Y|X = 2500) =? d) Find E(Y)and E(X).

#### Homework Answers

Answer #1

d)

where

a)

b)

so,

c)

similarly

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