problem 2

Let $N$ be the number of days in a randomly chosen year.

E (N) = \frac{3}{4} 365 + \frac{1}{4} 366 = 365.25

Var (N) = E (N^{2}) - {(E (N))}^{2} = \frac{3}{4} 36 5^{2} + \frac{1}{4} 36 6^{2} - 365.2 5^{2} = 0.1875