In some applications we are interested in the distribution of the maximum among a set of realization of random variables. Let us consider a set of n i.i.d. variables Ui, i = 1,... ,n, with uniform distribution on the unit interval [0,1]. Let X be their maximum: X = max{Ui, U2, ■ ■ ·, Un}. Prove that the CDF of X is Fx{x) = xn

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