Joint distribution
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In the study of probability, given two random variables X and Y, the joint distribution of X and Y is the distribution of X and Y together.
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[edit] The discrete case
For discrete random variables, the joint probability mass function can be written as Pr(X = x & Y = y). This is
Since these are probabilities, we have
[edit] The continuous case
Similarly for continuous random variables, the joint probability density function can be written as fX,Y(x, y) and this is
where fY|X(y|x) and fX|Y(x|y) give the conditional distributions of Y given X = x and of X given Y = y respectively, and fX(x) and fY(y) give the marginal distributions for X and Y respectively.
Again, since these are probability distributions, one has
[edit] Joint distribution of independent variables
If for discrete random variables 
for all x and y, or for continuous random variables 
for all x and y, then X and Y are said to be independent.
[edit] Multidimensional distributions
The joint distribution of two random variables can be extended to many random variables X1, ..., Xn by adding them sequentially with the identity
[edit] See also
[edit] External links
| This page uses content from the English-language version of Wikipedia. The original article was at Joint distribution. The list of authors can be seen in the page history. As with Psychology Wiki, the text of Wikipedia is available under the GNU Free Documentation License. |
