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$Y = X+N$ where $X,N$ are normally distributed with zero mean.

I know that $Y$ is also normally distributed with zero mean and sum of variances.

I don't know how to get $f(X|y)$ in order to calculate ${\rm E}(X|y)$.

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    See http://mathoverflow.net/questions/47168/ex-1-x-1-x-2-where-x-i-are-integrable-independent-infinitely-divisib for a generalization of this result.2010-11-24

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