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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Discrete and Combinatorial Mathematics An Applied Introduction
Authors: Ralph P. Grimaldi
5th edition
201726343, 978-0201726343
