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Let X1, ..., X5 ~ Gamma(1, 1), the unit exponential distribution, and let X(1), ..., X(5)...

Let X1, ..., X5 ~ Gamma(1, 1), the unit exponential distribution, and let X(1), ..., X(5) be the corresponding order statistics. Write the densities of X(2) and X(5) and the joint density of (X(2), X(5)). From these, compute the probabilities P(X(2) > 2), P(X(5) < 4), and P(X(5) - X(2) > 3).

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