Consider independent and identically distributed random samples, X₁,...,X_n of size n from a distribution with PDF:

f(x) = ( 1) / x^a if 1 x < ; 0 otherwise, where > 1.

Let Y_n = min{X₁ ,..., X_n }.

1. Find the PDF of the smallest order statistic Y_n . 2. Find the CDF of the smallest order statistic Y_n . 3. What is the limiting distribution for Y_n , as n ? 4. Find the limiting distribution for Yⁿ_n , as n (if it exists).