Let X and W be the working and subsequent repair times of a certain machine. Let Y

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Let X and W be the working and subsequent repair times of a certain machine.

Let Y = X +W and suppose that the joint probability density of X and Y is fX,Y (x, y) = λ2e

−λy , 0

(a) Find the density of X.

(b) Find the density of Y.

(c) Find the joint density of X and W.

(d) Find the density of W.

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