If I have x1,x2 iid normal with N(0,1)(adsbygoogle = window.adsbygoogle || []).push({});

and I want to find E(x1*x2 | x1 + x2 = x)

Can I simply say: x1 = x - x2 and thus

E(x1*x2 | x1 + x2 = x) =

E[ (x - x2)*x2) = E[ (x * x2) - ((x2)^2) ] <=>

x*E[x2] - E[x2^2] =

0 - 1 =

-1?

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# Conditional Expectation

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