Chapter 5, Problem 5.5STPE

The random variable X is said to be a discrete uniform random variable on the integers 1.2..... n if $P\left\{X=i\right\}=\frac{1}{n}i=1,2,\mathrm{...},n$.

For any nonnegative real number x, let in t(x) (sometimes written as [x]) be the largest integer that is less than or equal to x. Show that if U is a uniform random variable on (0, 1), then $X=\mathrm{int}\left(nU\right)+1$ is a discrete uniform random variable on 1. ....n.