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

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.