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Math Help - Marginal Distribution

  1. #1
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    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.
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  2. #2
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    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
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