11. Let X, Y1,...,Yn be independent exponential random variables; X having rate , and Yi having rate

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 j th 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.