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.

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- Aug 28th 2009, 11:18 PMSanzaMarginal 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 PMMoo
Hello,

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

for getting the joint pdf :

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

and here, we have $\displaystyle p_X(x)=1$ (if $\displaystyle x\in (0,1)$, 0 otherwise)

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

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

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