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About LinkBacksLet X and Y be random variables withfor
Findand
My solution:
a) First of all,, so I have
b) Here,and
, so I have
But according to the law of total expectation, they should be the same thing, so what am I doing wrong? Thank you!
Let X and Y be random variables with
Find
My solution:
a) First of all,
b) Here,
But according to the law of total expectation, they should be the same thing, so what am I doing wrong? Thank you!
part of this was asked in another question here
(a) Yes,=e^{-x})
BUT that is the marginal, hence the range is x>0
you no longer want x<y.
Plus the E(X) is a constant, which cannot have Y's in it.
E(X)=1, this is an exponential
(b) Yes,
and, y>0 a Gamma RV
So) =\int_0^{\infty}(y/2)ye^{-y}dy=(1/2)\int_0^{\infty}y^2e^{-y}dy=(1/2)\Gamma(3)=1.)
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