# Variable + Random Variable + Random Process

26/09/2011

**Variable**:**Random****Variable**: is a variable described by a probability density function (PDF)**Random Process**: is a function of time t. The function value is a random variable described by a PDF.

**Random Variable**: key features

Expectation value: E(x)

Variance: Var(x)

Covariance: Var(x,y)**Random Process**: key features

Expectation value: E[x(t)]

Variance: Var[x(t)]

Auto-correlation function: .

Cross-correlation function: .

The main **difference** between random variables and random processes is the auto-correlation function, which describes the change of the process over time. Another important feature is **power spectral density** (PSD) function. Power spectral density function is equivalent to auto-correlation function because they can be converted to each other using Fourier transformation.

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