Editing Probability density function (section)

===Corollary===

If the joint probability density function of a vector of {{mvar|n}} random variables can be factored into a product of {{mvar|n}} functions of one variable
<math display="block">f_{X_1,\ldots,X_n}(x_1,\ldots,x_n) = f_1(x_1)\cdots f_n(x_n),</math>
(where each {{math|''f<sub>i</sub>''}} is not necessarily a density) then the {{mvar|n}} variables in the set are all [[statistical independence|independent]] from each other, and the marginal probability density function of each of them is given by
<math display="block">f_{X_i}(x_i) = \frac{f_i(x_i)}{\int f_i(x)\,dx}.</math>