11. Let X, Y1, . . . ,Yn be independent exponential random variables; X having rate ,...
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11. Let X, Y1, . . . ,Yn be independent exponential random variables; X having rate λ, and Yi having rate μ. Let Aj be the event that the jth smallest of these n + 1 random variables is one of the Yi . Find p = P{X > maxi Yi}, by using the identity p = P(A1 · · ·An) = P(A1)P(A2|A1) · · · P(An|A1 · · ·An−1)
Verify your answer when n = 2 by conditioning on X to obtain p.
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