# Questions tagged [multivariate-normal-distribution]

The multivariate normal distribution, is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. (Also called, multivariate Gaussian)

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### Proving Equivalence between Multivariate distributions and Gaussian Bayesian Networks

I am studying Probabilistic Graphical Models by Daphne Koller. In Chap 7, the authors say the following. I can't convince myself of the highlighted part. Induction typically has a statement for n, ...
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### How to scale (in the range 0 to 1) and mathematically explain two mutually exclusive probabilities of a data point belonging to a normal distribution?

I have two set of n-dimensional multivariate data, with the assumption that both set of data is normally distributed. When I get a new data point, my goal is to classify it into one of the two sets. ...
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### truncation of bivariate normal under quadratic condition

Consider a complex normal variable $Z \sim \mathcal{CN}(\mu,2\sigma^2)$ with real component $X \sim \mathcal{N}(\mu,\sigma^2)$ and imaginary component $Y \sim \mathcal{N}(0,\sigma^2)$. We can write ...
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### Conditional distributions of correlated normal random variables

Suppose that $X$ and $Y$ are normally distributed with mean zero and nonzero covariance. I want to know the distributions of $X | X - Y > c$ and $Y | X - Y > c$, which I believe should be ...