$X$ takes the values 0, 1 and 2 with probabilities 0.3, 0.5 and 0.2. What is $\text{Var}(X)$?

Explanation

1. 01

   $E(X) = 0.9$ and $E(X^{2}) = 0 \times 0.3 + 1 \times 0.5 + 4 \times 0.2 = 1.3$.

2. 02

   $\text{Var}(X) = E(X^{2}) - [E(X)]^{2} = 1.3 - 0.81 = 0.49$.