problem 5

Let $X \sim DUniform (n)$ .

E (X) = \frac{1}{n} n \sum i = 1 i = \frac{1}{2} (n + 1)

Var (X) = E (X^{2}) - {(E (X))}^{2} = \frac{1}{n} n \sum i = 1 i^{2} - {(\frac{1}{2} (n + 1))}^{2} = \frac{1}{6} (n + 1) (2 n + 1) - \frac{1}{4} {(n + 1)}^{2}