Let X and Y by two independent identically distributed normal random variables with mean 1 and variance 1. Find c so that E[c|X-Y|] = 1.

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I went with the 'simple' route

E[c|X-Y|] = cE[X-Y] + cE[X+Y] = 0 + c(1+1) = 2c

And 2c = 1 so c = 1/2

But that was wrong...

I know there's a 1/sqrt(2pi) in the normal distribution but I can't see how that pi can get to the numerator in those integrals...

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Answer is sqrt(pi)/2