Q.The expected value of the sum of two numbers obtained when two fair dice are rolled is ______.

The mean $E(X)=\mu=\sum x_i p_i$ (discrete) or $\int x f(x)\,dx$ (continuous) is the probability-weighted average value of $X$. The variance $\operatorname{Var}(X)=\sigma^2=E(X^2)-[E(X)]^2$ measures spread, with standard deviation $\sigma=\sqrt{\operatorname{Var}(X)}$. Useful rules: $E(aX+b)=aE(X)+b$ and $\operatorname{ …