Introduction to Probability · Problem 5.1.6

Distributions and Densities — Grinstead & Snell

Mathematics — Probability · discrete-distributions

Problem

Let

X_1, X_2, \ldots, X_n

n

mutually independent random variables, each of which is uniformly distributed on the integers from 1 to

k

. Let

Y

denote the minimum of the

X_i

's. Find the distribution of

Y