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 $$ \begin{equation*} \langle x^n \rangle \equiv \int\! x^n p(x)\,dx \end{equation*} $$