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Jointly continuous RVs have the following properties:
Example
Consider the RV X with uniform distribution over [0,1]:
Suppose h(x) = x3/2:
Consider the RV X with binomial distribution and parameters N = 2 and p = 0.2. Support of X is {x0 = 0, x1 = 1, x2 = 2}.
Suppose h(x) = x1/2:
Jointly Discrete RVs
Two jointly discrete RVs X and Y are characterized by a support:
a joint PMF {pi,j} for all i and j, and a joint CDF given by:
with the following properties:
The PDFs of the individual absolutely continuous RVs are determined from the joint PDF by:
The PMFs of the individual absolutely discrete RVs are determined from the joint PMF by:
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