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$X$ is a random variable, which is not constant. $E[X]=0$. $E[X^4] \leq 2(E[X^2])^2$. Let $Y$ be given by: $P(Y=E[X|X \geq 0]) = P(X \geq 0)$ and $P(Y=E[X|X \lt 0]) = P(X \lt 0)$.

Do we necessarily have $E[Y^4] \leq 2(E[Y^2])^2$?

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    Can you provide some background for this question?2010-12-21

2 Answers 2