- #1
Brandon1994
- 9
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Homework Statement
If X1 is uniform on [0,1], and, conditional on X1, X2, is uniform on [0,X1], find the joint and marginal distributions of X1 and X2
Homework Equations
conditional joint distribution
The Attempt at a Solution
f(x1|x2) = 1/x1 (for 0<x2<x1)
f(x1) = 1 ( for 0<x1<1)
then
F(x1,x2) = Integrate (1/x1) from {x2,0,x2}{x1,0,x1}
I get an ln(0) when i try to integrate however
for the marginal distribution of x2, i get X2~[0,X1] //i am not sure if that's the answer they are looking for, if i try to write an explicit density function for X2 i get that the density is infinity, again due to the ln (0) term.
Thanks