Mean

Definition: The mean of a stochastic process $v(n)$ at time $n$ is defined as the expected value of $v(n)$ :

$$\mu_{v(n)} \isdef E\{v(n)\} \isdef \int_{-\infty}^\infty x p_{v(n)}(x) dx$$ (C.16)

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

For a stationary stochastic process $v$ , the mean is given by the expected value of $v(n)$ for any $n$ . I.e., $\mu_v = E\{v(n)\}$ for all $n$ .