(X) and (Y) are independent, exponentially with parameter (lambda=1) distributed random variables. Determine (1) (E(X-Y)), (2) (E(|X-Y|)),...

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\(X\) and \(Y\) are independent, exponentially with parameter \(\lambda=1\) distributed random variables. Determine

(1) \(E(X-Y)\),

(2) \(E(|X-Y|)\), and

(3) distribution function and density of \(Z=X-Y\).

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