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Let Xi, i=1,...,n be independent exponential r.v. with mean 1/ui. Define Yn=min(X1,...,Xn), Zn=max(X1,...,Xn). 1. Define the...

Let Xi, i=1,...,n be independent exponential r.v. with mean 1/ui. Define Yn=min(X1,...,Xn), Zn=max(X1,...,Xn).

1. Define the CDF of Yn,Zn

2. What is E(Zn)

3. Show that the probability that Xi is the smallest one among X1,...,Xn is equal to ui/(u1+...+un)

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