Question: Let { X n } n = 1 be a sequence of independent and identically distributed random variables all with the uniform distribution on the

Let{Xn}n=1 be a sequence of independent

and identically distributed random variables all

with the uniform distribution on the interval

[0, 1]. For each n letYn=max{X1,...,Xn} .

Show that the sequence{Yn}n=1 converges in

probability to a constant and find the constant.

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