Let $h(x)$ be an arbitrary continuous function on the domain of the stochastic variable $X$ whose PDF is $p(x)$. We define the expectation value of $h$ with respect to $p$ as follows $$\begin{equation} \langle h \rangle_X \equiv \int\! h(x)p(x)\,dx \tag{2} \end{equation}$$ Whenever the PDF is known implicitly, like in this case, we will drop the index $X$ for clarity. A particularly useful class of special expectation values are the moments. The $n$-th moment of the PDF $p$ is defined as follows $$\begin{equation*} \langle x^n \rangle \equiv \int\! x^n p(x)\,dx \end{equation*}$$