A coin is tossed once, and $X = 1$ for a head and $X = 0$ for a tail. What is $\text{Var}(X)$?

Explanation

1. 01

   $E(X) = \frac{1}{2}$ and $E(X^{2}) = \frac{1}{2}$.

2. 02

   $\text{Var}(X) = \frac{1}{2} - \frac{1}{4} = \frac{1}{4}$.