Question

Find the expected value and variance of \( X \) for the following p.m.f: \[ \begin{array}{|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 \\ \hline P(X) & 0.2 & 0.3 & 0.1 & 0.15 & 0.25 \\ \hline \end{array} \]

Hint:

To calculate the variance, use the formula \( \text{Variance} = E(X^2) - (E(X))^2 \), where \( E(X^2) \) is the expected value of \( X^2 \).