This video reviews the probability density function (pdf) for the
multivariate Gaussian random variable. This pdf is then derived by
developing the isotropic multivariate Gaussian, and then transforming
through a linear transformation. The effect of the linear transformation
on both the pdf and second-order statistical descriptors are
considered. The video considers how the bivariate Gaussian density
depends on the correlation coefficient, and how its orientation changes
with this coefficient. Finally, the video considers key properties of
the multivariate Gaussian, such as the fact that the linear
transformation of a Gaussian is a Gaussian; that the marginal of a
Gaussian is a Gaussian; and that the conditional distribution of a
Gaussian is a Gaussian. The role of the multivariate Gaussian
distribution within statistical signal processing is also discussed.
PGEE11164 Probability, Estimation Theory, and Random Signals Lectures -- School of Engineering, University of Edinburgh. Copyright James R. Hopgood and University of Edinburgh, Scotland, United Kingdom (UK). 2020.
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