A coin is tossed twice, and $X$ is the number of heads. What is $\text{Var}(X)$?

Explanation

1. 01

   $P(0) = \frac{1}{4}$, $P(1) = \frac{1}{2}$, $P(2) = \frac{1}{4}$, so $E(X) = 1$ and $E(X^{2}) = \frac{1}{2} + 1 = \frac{3}{2}$.

2. 02

   $\text{Var}(X) = \frac{3}{2} - 1 = \frac{1}{2}$.