Probability and Random Processes

Expected Value

Variance

Stochastic Processes

Ensembles of random functions of time (or space) are referred to as stochastic processes. For fixed time, a stochastic process becomes a random variable. Every sample of a stochastic process is a time function.

The statistics of a stochastic process may be evaluated in a similar mannar to that of a random variable. For example, the mean value is given as

Time Average

Time averaging over an interval (0,T) is defined as