Question: Let Xi, i = 1,...,n be independent and identically distributed random variables, of law U([0,]), a uniform law on [0,]. Let Y = max{X1,...,Xn}. 1.

Let Xi, i = 1,...,n be independent and identically distributed random variables, of law U([0,]), a uniform law on [0,]. Let Y = max{X1,...,Xn}.

1. By observing that Y y if and only if Xk y for all 1 k n, compute the cumulative distribution function of Y .

2. Compute the density function of Y .

3. Find such that := max{X1,...,Xn} is an unbiased estimator of .

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