I wanted to know if there is a way to calculate the mean of a multivariate normal distribution when a certain variable is held constant. For example, if I had a continuous bivariate normal distribution of variables $x$ and $y$, s.t. $X \sim N_2(\mu, \Sigma)$, how can I find the mean of $y$ when $x=\alpha$? Is there a simple calculus approach?
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kjetil b halvorsen
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1That's the conditional marginal distribution of $y$, denoted as $P(y|x=\alpha)$. – Spätzle Aug 17 '21 at 05:15