[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Let [math]X_1,\ X_2,\ \ldots,\ X_n[/math] be [math]n[/math] mutually independent

random variables, each of which is uniformly distributed on the integers from 1 to [math]k[/math]. Let [math]Y[/math] denote the minimum of the [math]X_i[/math]'s. Find the distribution of [math]Y[/math].