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What is closed form equation for the tail probability of multivariate normal distribution ?

y ~ $\mathcal{N}$($0$, $\sigma^2I_n$ ) ; y $\in\mathbb{R}^n$

Pr(y > $\gamma$) = $\int_\gamma^\infty$ pr(y) d y ; $\gamma\in\mathbb{R}$

-Sun

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    You could ask yourself where your $\gamma$ lives? Is it in $\mathbb{R}$ (as the appearance of $\gamma$ as a bound of the integral seems to indicate) or in $\mathbb{R}^n$ (as the expression $\mathbb{y}>\gamma$ suggests)? This cannot be both...2011-02-04
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    scope of $\gamma$ added...2011-02-04
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    Then what does $\mathbb{y}>\gamma$ means? You cannot have it both ways.2011-02-04
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    It might mean that each component of $\mathbf{y}$ is bigger than $\gamma$. That would make sense.2011-02-04
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    @Raskolnikov Sure, it *might*... Then one wonders about the one-dimensional integral on the RHS. My point is that the OP should make the question clearer.2011-02-04

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