Stationary & WSS Processes

Instructions

A random process is defined by its statistical properties over time. Key classifications include:

Strict-Sense Stationary (SSS): The joint probability distribution of any set of samples is invariant with respect to a shift in time. This is the strongest form of stationarity.
Wide-Sense Stationary (WSS): A weaker form of stationarity where the mean of the process is constant, and the autocorrelation function depends only on the time lag (τ), not on absolute time. All SSS processes are WSS, but the reverse is not always true.
Non-Stationary: A process that does not meet the criteria for WSS. Either its mean is a function of time, or its autocorrelation depends on absolute time as well as the time lag.

Select a "Mystery Process" to begin.
An equation defining a random process X(t) will be displayed, along with definitions for all its variables.
Analyze the equation to determine if the process is SSS, WSS, or Non-Stationary.
Select your answer from the dropdown and press "Submit Answer" to see a detailed explanation with mathematical proofs and plots.