Let X and Y be random variables with for
Find and
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 for
Find and
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!
part of this was asked in another question here
(a) Yes,
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