\begin{definition}[Definition:Expectation/Absolutely Continuous]
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space. 
Let $X$ be an absolutely continuous random variable on $\struct {\Omega, \Sigma, \Pr}$.
Let $f_X$ be the probability density function of $X$. 
The '''expectation of $X$''', written $\expect X$, is defined by: 
:$\ds \expect X = \int_{-\infty}^\infty x \map {f_X} x \rd x$ 
whenever: 
:$\ds \int_{-\infty}^\infty \size x \map {f_X} x \rd x < \infty$
\end{definition}