Variance

Definition: The variance or second central moment of a stochastic process $v(n)$ at time $n$ is defined as the expected value of $\left\vert v(n)-\mu_{v(n)}\right\vert^2$ :

$$\sigma^2_{v(n)} \isdef E\{\left\vert v(n)-\mu_{v(n)}\right\vert^2\} \isdef \int_{-\infty}^\infty \left\vert v(n)-\mu_{v(n)}\right\vert^2 p_{v(n)}(x) dx$$ (C.19)

where $p_{v(n)}(x)$ is the probability density function for the random variable $v(n)$ .

For a stationary stochastic process $v$ , the variance is given by the expected value of $\left\vert v(n)-\mu_v\right\vert^2$ for any $n$ .