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If $X = [X_1,\dots,X_n]$ is follows a multivariate normal distribution $\mathcal{N}(\mu,\Sigma)$, are there any (closed form) results known for the distribution of $[X_1,\dots,X_i \mid l_{i+1} < X_{i+1} < u_i ,\dots, l_n < X_n < u_n]$?

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