The random variable X is said to be a discrete uniform random variable on the integers 1,2...

The random variable X is said to be a discrete uniform random variable on the integers 1,2,..., n if For any nonnegative real number x, let Int(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 = Int(nU) + 1 is a discrete uniform random variable on 1,.. .,n.