Suppose that (X) is uniformly distributed on the surface of the unit sphere in (mathbb{R}^{d}), and that

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Suppose that \(X\) is uniformly distributed on the surface of the unit sphere in \(\mathbb{R}^{d}\), and that \(Y \sim N\left(X, \sigma^{2} I_{d}ight)\) is observed. Show that Eddington's formula reduces to the projection \(E(X \mid Y)=Y /\|Y\|\).

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