Question: Let X 1 , X 2 , . . . , X n are i.i.d. U ( 0 , ) and X ( n )

LetX1,X2,...,Xn are i.i.d.U(0,) and X(n)=maxXi. Show that X(n) converges in probability to . Furthermore, show that n(X(n))converges in distribution to an Exponential ( 1/ ) random variable.1in

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