Editing Joint probability distribution (section)

== Marginal probability distribution ==
{{Main|Marginal distribution}}
If more than one random variable is defined in a random experiment, it is important to distinguish between the joint probability distribution of X and Y and the probability distribution of each variable individually. The individual probability distribution of a random variable is referred to as its marginal probability distribution. In general, the marginal probability distribution of X can be determined from the joint probability distribution of X and other random variables.

If the joint probability density function of random variable X and Y is  <math>f_{X,Y}(x,y)</math> , the marginal probability density function of X and Y, which defines the [[marginal distribution]], is given by:

<math>f_{X}(x)= \int f_{X,Y}(x,y) \; dy    </math>
<br>
<math>f_{Y}(y)= \int f_{X,Y}(x,y)  \; dx   </math>

where the first integral is over all points in the range of (X,Y) for which X=x and the second integral is over all points in the range of (X,Y) for which Y=y.<ref>{{Cite book|title=Applied statistics and probability for engineers|last=Montgomery, Douglas C.|others=Runger, George C.|isbn=978-1-118-53971-2|edition=Sixth|location=Hoboken, NJ|oclc=861273897|date = 19 November 2013}}</ref>