12. If Xi, i = 1, 2, 3, are independent exponential random variables with rates i, i...
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12. If Xi, i = 1, 2, 3, are independent exponential random variables with rates
λi, i = 1, 2, 3, find
(a) P{X1 < X2 < X3},
(b) P{X1 < X2|max(X1, X2, X3) = X3},
(c) E[maxXi|X1 < X2 < X3],
(d) E[maxXi].
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