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The probability that an event A will occur, when another event B is known to occur or to have occurred. It is commonly denoted by P(A|B).
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Conditional distribution of a multivariate Gaussian given $X_1 = ... = X_n$
What is the distribution of $(X_1, ..., X_n)^T \sim \mathcal{N}(\mu, \Sigma)$ given that $X_1 = ... = X_n$?