Assume X_1, ..., X_n are iid. according to an exponential distribution with density

fX(x)=exp(x)x>0

LetMn=max(X1,...,Xn)

i) show thatMnlog(n)dM, where M has c.d.fP{My}=exp{exp(y)}

ii) deduce that log(n)Mnconverges in probability and identify the limit