Assessment |
Biopsychology |
Comparative |
Cognitive |
Developmental |
Language |
Individual differences |
Personality |
Philosophy |
Social |

Methods |
Statistics |
Clinical |
Educational |
Industrial |
Professional items |
World psychology |

**Statistics:**
Scientific method ·
Research methods ·
Experimental design ·
Undergraduate statistics courses ·
Statistical tests ·
Game theory ·
Decision theory

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.

## Contents

## The discrete case[edit | edit source]

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

## The continuous case[edit | edit source]

Similarly for continuous random variables, the **joint probability density function** can be written as *f*_{X,Y}(*x*, *y*) and this is

where *f*_{Y|X}(*y*|*x*) and *f*_{X|Y}(*x*|*y*) give the conditional distributions of *Y* given *X* = *x* and of *X* given *Y* = *y* respectively, and *f*_{X}(*x*) and *f*_{Y}(*y*) give the marginal distributions for *X* and *Y* respectively.

Again, since these are probability distributions, one has

## Joint distribution of independent variables[edit | edit source]

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.

## Multidimensional distributions[edit | edit source]

The joint distribution of two random variables can be extended to many random variables *X*_{1}, ..., *X*_{n} by adding them sequentially with the identity

## See also[edit | edit source]

## External links[edit | edit source]

This page uses Creative Commons Licensed content from Wikipedia (view authors). |