Find the mean and the variance of the uniform probability distribution given by

\[f(x)=\frac{1}{n} \quad \text { for } x=1,2,3, \ldots, n\]

The sum of the first \(n\) positive integers is \(n(n+1) / 2\), and the sum of their squares is \(n(n+1)\) \((2 n+1) / 6\).]