5.8. Let U, U, ..., U be independent uniformly distributed random variables on the unit interval [0, 1]. Define the minimum V = min{U, U,,, U}. 2

(a) Show that Pr{V> v} = (1-v)" for 0 y 1.

(b) Let W, nV,,. Show that Pr{ W> w} = [1 (w/n)]" for 0 w n, and thus lim Pr{W, w} = e"" for w 0.