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I have a few questions where I'm trying to show if things are true or false. I'll say upfront that these are homework so I'd rather not get the entire answer just someone to point me in the right direction. So here we go,

If $y = x \beta + e\text{ and } E(e|x) = 0, \text{ then } E(x^2e) = 0$.

If $y = x \beta + e,\text{ and }E(xe) = 0,\text{ then } E(x^2e) = 0$

Thanks for any help.

Edit: Solved then removed one of them.

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    If you solve one of them, you could leave the question up and post your answer as a solution. Someone else might be interested in how you did it.2011-09-15

1 Answers 1

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Hints:

1) The equations involving $y$ are irrelevant, since $y$ doesn't appear in the conclusion.

2) A fundamental principle is the "Theorem of Total Expectation": $E[ E[X | Y]] = E[X]$.

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    For (2.), what happens if $e$ is constant? Can you find an example where $E(x) = 0$ but $E(x^2) \ne 0$?2011-09-15