# Marginal Distribution

• Aug 28th 2009, 11:18 PM
Sanza
Marginal Distribution
Suppose that X ~ Uniform(0,1). After obtaining a value of X we generate
Y|X = x ~ Uniform(x,1). Find the marginal distribution of Y.
• Aug 28th 2009, 11:43 PM
Moo
Hello,

Look here : Conditional probability distribution - Wikipedia, the free encyclopedia

for getting the joint pdf :

$p_{X,Y}(x,y)=p_{Y|X}(y|x) \cdot p_X(x)$

and here, we have $p_X(x)=1$ (if $x\in (0,1)$, 0 otherwise)
and $p_{Y|X}(y|x)=\frac{1}{1-x}$ (if $y\in (x,1)$, 0 otherwise)

so the joint pdf is $\frac{1}{1-x} \text{ if } x\in (0,1) \text{ and } y\in(x,1)$

then find the region described by x, with respect to y.
and integrate with respect to x over this region.

try to do that and let us know if you can't do it