Education
 

Joint distribution

From Psychology Wiki

Community portal · Tasks to do · News · Help

Clinical · Educational · Ind&Org · Other fields · Professional · Transpersonal · World

Assessment | Biopsychology | Comparative | Cognitive | Developmental | Language
Personality | Philosophy | Research Methods | Social | Statistics

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

[edit] The discrete case

For discrete random variables, the joint probability mass function can be written as Pr(X = x & Y = y). This is

math

Since these are probabilities, we have

math

[edit] The continuous case

Similarly for continuous random variables, the joint probability density function can be written as fX,Y(xy) 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

math

[edit] Joint distribution of independent variables

If for discrete random variables math for all x and y, or for continuous random variables math 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

math

[edit] See also

[edit] External links

Smallwikipedialogo.png 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.