Linear transformations and Gaussian random vectors Remember, n-vectors are the same as n × 1 matrices Let X a random n-vector We let E(X)
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[PDF] Gaussian Random Vectors
Vectors 1 The multivariate normal distribution Let X := (X1 X ) be a random vector We say that X is a Gaussian random vector if we can write
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If the components of an n-rv are independent and identically distributed (IID), we call the vector an IID n-rv 3 3 2 IID normalized Gaussian random vectors An
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10 oct 2008 · The concept of the covariance matrix is vital to understanding multivariate Gaussian distributions Recall that for a pair of random variables X
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Similarly to the scalar case, the pdf of a Gaussian random vector is completely characterized by its first and second moments, the mean vector and the covariance
[PDF] Lecture 1 Random vectors and multivariate normal distribution
Lemma 2 The p × p matrix Σ is a covariance matrix if and only if it is non-negative definite 1 2 Multivariate normal
[PDF] Linear transformations and Gaussian random vectors Remember, n
Linear transformations and Gaussian random vectors Remember, n-vectors are the same as n × 1 matrices Let X a random n-vector We let E(X)
Gaussian Random Variables
standard Gaussian random vector 4 The Gaussian Concentration Inequality The Gaussian Poincaré inequality gives a bound on the variance of a function of
[PDF] The Gaussian distribution
Again, the vector µ speci es the mean of the multivariate Gaussian distribution The matrix Σ speci es the covariance between each pair of variables in x:
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