A particularly useful class of special expectation values are the moments. The $n$-th moment of the PDF $p$ is defined as follows:

$$\langle x^n\rangle \equiv \int\! x^n p(x)\,dx$$

The zero-th moment $\langle 1\rangle$ is just the normalization condition of $p$. The first moment, $\langle x\rangle$, is called the mean of $p$ and often denoted by the letter $\mu$:

$$\langle x\rangle = \mu \equiv \int\! x p(x)\,dx$$