Editing Marginal distribution (section)

==Multivariate distributions==

[[File:MultivariateNormal.png|thumb|300px|Many samples from a bivariate normal distribution. The marginal distributions are shown in red and blue. The marginal distribution of X is also approximated by creating a histogram of the X coordinates without consideration of the Y coordinates.]]

For [[multivariate distribution]]s, formulae similar to those above apply with the symbols ''X'' and/or ''Y'' being interpreted as vectors. In particular, each summation or integration would be over all variables except those contained in ''X''.<ref name=":1">{{Cite book|title=A modern introduction to probability and statistics : understanding why and how|date=2005|publisher=Springer|others=Dekking, Michel, 1946-|isbn=9781852338961|location=London|oclc=262680588}}</ref>

That means, If ''X''<sub>1</sub>,''X''<sub>2</sub>,…,''X<sub>n</sub>'' are '''discrete [[random variable]]s''', then the marginal [[probability mass function]] should be
<math display="block">p_{X_i}(k)=\sum p(x_1,x_2,\dots,x_{i-1},k,x_{i+1},\dots,x_n);</math>
if ''X''<sub>1</sub>,''X''<sub>2</sub>,…,''X<sub>n</sub>'' are '''continuous random variables''', then the marginal [[probability density function]] should be
<math display="block">f_{X_i}(x_i)=\int_{-\infty}^{\infty}\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \cdots \int_{-\infty}^{\infty} f(x_1,x_2,\dots,x_n) dx_1 dx_2 \cdots dx_{i-1} dx_{i+1} \cdots dx_n .</math>