$X$ takes the values 1, 2 and 3 with probabilities 0.25, 0.5 and 0.25. What is $\text{Var}(X)$?

Explanation

1. 01

   $E(X) = 0.25 + 1 + 0.75 = 2$ and $E(X^{2}) = 0.25 + 2 + 2.25 = 4.5$.

2. 02

   $\text{Var}(X) = 4.5 - 2^{2} = 0.5$.