Editing Marginal distribution (section)

=== Marginal cumulative distribution function ===
Finding the marginal [[cumulative distribution function]] from the joint cumulative distribution function is easy. Recall that:

* For '''discrete [[random variable]]s''', <math display="block">F(x,y) = P(X\leq x, Y\leq y)</math>
* For '''continuous random variables''', <math display="block">F(x,y) = \int_{a}^{x} \int_{c}^{y} f(x',y') \, dy' dx'</math>

If ''X'' and ''Y'' jointly take values on [''a'', ''b''] × [''c'', ''d''] then

:<math>F_X(x)=F(x,d)</math> and <math>F_Y(y)=F(b,y)</math>

If ''d'' is ∞, then this becomes a limit <math display="inline">F_X(x) = \lim_{y \to \infty} F(x,y)</math>. Likewise for <math>F_Y(y)</math>.