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Joint Distribution


The joint distribution of random variables X_1,...,X_n assigns probabilities to events involving the variables simultaneously. For two real random variables it is determined by the joint distribution function

 F_(X,Y)(x,y)=Pr(X<=x, Y<=y).

In the discrete case, the joint probability mass function is p(x,y)=Pr(X=x,Y=y). In the continuous case, when a joint probability density function f exists, probabilities are integrals of f over subsets of the plane. Summing or integrating out variables gives the marginal distributions.


See also

Joint Distribution Function, Marginal Distribution

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References

Casella, G. and Berger, R. L. Statistical Inference, 2nd ed. Pacific Grove, CA: Duxbury, 2002.

Cite this as:

Weisstein, Eric W. "Joint Distribution." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/JointDistribution.html

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