Basic Concepts of Random Processes
Definitions :: Ergodicity :: Autocorrelations :: Sinusoidal :: Poisson :: Gaussian :: Properties :: Spectra :: Cases :: Random :: Independent
Basic definitions and concepts
 If is a singleton (one element) then is a r.v.
 If , then is a bivariate r.v.
 If consists of a finite number of elements, then is a random vector.
 If is countable, then is a random sequence.
Three interpretations of a r.p.

A collection of waveforms that occur randomly. That is, it is
defined on some probability space. For each
there is a corresponding waveform
as a
function of
with
fixed.
Think of having a big bag of waveforms. We reach into the bag and pick out a waveform  a function of  at random.
 A collection of random variables. In this case, that is, for each fixed , we have a random variable .
 A realvalued function of two variables .
A realization is just a function. It does not exhibit the randomness.
We will assume this set completely characterizes the statistical distribution of the process.
Strict stationarity is a fairly strong condition, and we don't
necessarily need it always.