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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for getting the joint pdf :
and here, we have (if , 0 otherwise)
and (if , 0 otherwise)
so the joint pdf is
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