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Now, consider joint density of $X, Y$ : $$ f_{X, Y}(x, y)=\left\{\begin{array}{l} \frac{1}{\pi} ; X^2+Y^2<1 \\ 0 ; \text { Otherwise } \end{array}\right. $$ Derive $E(Y \mid X)$.

I know how to calculate E(Y), but how do you calculate the conditional expectation? please help

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  • $\begingroup$ Find the conditional density. $\endgroup$
    – StubbornAtom
    Commented Oct 6, 2022 at 5:47
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    $\begingroup$ Hi. Please add self-study tag. Problems like these warrant minimal research efforts. As @StubbornAtom indicated, proceed with this and update your post if you stumble. $\endgroup$
    – User1865345
    Commented Oct 6, 2022 at 5:51
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    $\begingroup$ Questions of this type can be answered either by (i) applying the analytic formulas for conditional densities and expectation from statistical theory or (ii) geometrically from the shape of the joint density. In this case the answer is immediately obvious from the geometry if you know how to think about it. $\endgroup$
    – Gordon Smyth
    Commented Oct 6, 2022 at 5:56

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