# Multivariate normal distribution. Distribution of the sample mean conditioned to a given event

Let $\vec{X}\sim N_d(\vec{\mu},\Sigma)$.  If $\vec{\mu}=\mu \vec{1}$ and $\Sigma=\sigma^2 I_d$, find the distribution of $\overline{X}_d$ conditioned to the event $$\{d\max\{X_1,\dots,X_d\}\in B\},$$ where $B$ is an arbitrary borel set.

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