Mean and Variance

Population Mean and Population Variance

Recall that for a discrete random variable $X$, with possible outcomes $\{x_k^{\ast }{\}}_{k=1}^K$, where $K$ can be finite or countably infinite

The population mean of a continuous random variable $X$, denoted ${\mu }_X$ or $E(X)$ is given by:

${\mu }_X=E(X)={\int }_{-\infty }^{\infty }x{f}_X(x)dx$

Recall that for a discrete random variable $X$:

${\sigma }_X^2=\text{Var}(X)=E[(X-{\mu }_X{)}^2]={\int }_{-\infty }^{\infty }($