- #1
Joshuarr
- 23
- 1
Homework Statement
This is an example in a textbook; it already has the solution. I don't understand how E[X|Y] was obtained though. So my question is how do I calculate E[X|Y] from the information given?
http://img689.imageshack.us/img689/484/20120413134552578.jpg
http://img27.imageshack.us/img27/770/20120413134653906.jpg
This last part is probably not needed to solve the problem, I think. But I am adding it for completeness and context.
http://img801.imageshack.us/img801/3802/20120413141622958.jpg
E[X] is the expected value, or mean, of X.
Homework Equations
[tex] E[X|Y] = \int_{-\infty}^{\infty} x f_{X|Y}(x|y)dx [/tex]
Law of Total Variance: var(X) = E[var(X|Y)] + var(E[X|Y])
The Attempt at a Solution
I don't really understand how X is dependent on Y. It seems to me that Y is dependent on X! I'm really lost with this material, though. I don't have fX|Y(x|y) and I think that E[X|Y] is independent of Y, which would imply that E[X|Y] = E[X].
[tex]E[X] = 1/2\int_{0}^{1} x dx + 1/4\int_{1}^{3} x dx
= 1/2*1 + 1/4*2 = 1?[/tex]
E[X|Y] is supposed to be a random variable that is a function of Y though. I just don't see how Y plays any part in the computation.
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