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The following are properties of a PMF:
Example
A discrete RV X that is binomially distributed with parameters N and 0 <= p <= 1 with support x0 = 0, x1 = 1, ..., xN = N and a PMF:
Expected Value
The expected value (i.e. mean or statistical average) of a RV X is given by:
Autocorrelation
The autocorrelation of a RV X is given by:
nth Moment
The nth moment of a RV X is given by:
Variance
The variance of a RV X is given by:
Standard Deviation
The standard deviation of a RV X is given by:
Expected Value of a Function
The expected value of a function of a RV X is given by:
Joint Characterization of RVs
Two jointly (absolutely) continuous RVs X and Y are defined by a joint PDF:
and a joint CDF:
Jointly continuous RVs have the following properties:
