Assignment:
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{U1, U2,…, Un}. Prove that the CDF of X is Fx{x) = xn.
Provide complete and step by step solution for the question and show calculations and use formulas.