Expected Value

The expected value for $X$ can be denoted with $E(X)$, $\bar{X}$, $m_x$ or $\mu$

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

And for a function $g(X)$

$$E(x)={\int }_{-\infty }^{\infty }g(x)f_X(x)dx$$

Where $f_X(x)$ is the Probability Density Function