Consider independent and identically distributed random samples, X1,...,Xn of size n from a distribution with PDF f(x) = (? ?1)/x? if 1 ?x 1. Let Yn = min{X1,...,Xn}. 1. Find the PDF of the smallest order statistic Yn. 2. Find the CDF of the smallest order statistic Yn. 3. What is the limiting distribution for Yn, as n ??? 4. Find the limiting distribution for Y nn , as n ?? (if it exists).

3. (10 pts) Consider independent and identically distributed random samples, X], ..., X, of size n from a distribution with PDF f(x) = (@ -1)/c" if 1 1. Let Y, = min{ X1, ..., Xn). 1. Find the PDF of the smallest order statistic Y. 2. Find the CDF of the smallest order statistic Y,. 3. What is the limiting distribution for Y,, as n -> co? 4. Find the limiting distribution for Y", as n -> co (if it exists)