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Just want to confirm this. It's past mid-night and my brain is not working.

LEt $\Phi(x,y)$ and $\phi(x,y)$ be the CDF and PDF of bi-variate normally distributed variables.

Then

$\int_{b_{i-1}}^{b_i} \int_{a_{i-1}}^{a_i} \phi(x,y) dx dy = \Phi(a_i,b_i)-\Phi(a_{i-1},b_i)-\Phi(a_i,b_{i-1})+\Phi(a_{i-1},b_{i-1}) $

Amatya
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1 Answers1

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Yeah that's true - the reason is, you want only the finite rectangular region bounded by the $a_j$ and $b_j$ and you get this from the infinite regions coming from the CDF as you did.

amakelov
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