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I don't really know how to start proving this question.

Let $\xi$ and $\eta$ be random variables with $E(\xi)=E(\eta)=0$, $V(\xi)=V(\eta)=1$, and correlation coefficient $r$. Show that $$ E(\max(\xi^2,\eta^2))\leq1+\sqrt{1-r^2}. $$ Does anyone here have any idea for starting this question please?

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    Any luck with the answer below?2012-05-13

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