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## Homework Statement

Suppose that X=time to failure for a component has an exponential distribution with lambda =.25. Suppose that 9 of the components are selected and their failure times noted. Compute the probability that 3 of the components fail between times 1 and 2, and 4 of the components fail between times 2 and 3. Assume that the failure times are independent.

## Homework Equations

Exponential Distribution: f(x;λ)=λe

^{-xλ}

## The Attempt at a Solution

F(x,y)=∫∫0.25(e^(-x/4)*e^(-y/4))dxdy

I solved these over the intervals 2 to 1 and 3 to 2, and came up with F(1<x<2,2<y<3)=0.0925 as a solution for the probability that a component will fail. However, I'm not sure how to apply this to the 3/9 and 4/9 attempts. Am I even on the right track here?