Transcription of The Multivariate Gaussian Distribution
{{id}} {{{paragraph}}}
Example: quiz answers
The Multivariate Gaussian Distribution
The Multivariate Gaussian DistributionChuong B. DoOctober 10, 2008A vector-valued random variableX= X1 Xn Tis said to have amultivariatenormal (or Gaussian ) distributionwith mean Rnand covariance matrix Sn++1if its probability density function2is given byp(x; , ) =1(2 )n/2| |1/2exp 12(x )T 1(x ) .We write this asX N( , ). In these notes, we describe Multivariate Gaussians and someof their basic Relationship to univariate GaussiansRecall that the density function of aunivariate normal (or Gaussian ) distributionisgiven byp(x; , 2) =1 2 exp 12 2(x )2 .Here, the argument of the exponential function, 12 2(x )2, is a quadratic function of thevariablex.
The Multivariate Gaussian Distribution Chuong B. Do October 10, 2008 A vector-valued random variable X = X1 ··· Xn T is said to have a multivariate normal (or Gaussian) distribution with mean µ ∈ Rnn ++ 1 if its probability density function2 is given by p(x;µ,Σ) = 1 (2π)n/2|Σ|1/2 exp − 1 2 (x−µ)TΣ−1(x−µ) . of their basic ...
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: