Chapter 2: Random Vectors Morris L. Eaton, Multivariate Statistics: A Vector Space Approach (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2007), 2007 Bounds on the Maximum Sample Size of a Bayes Sequential Procedure Ray, S. N., Annals of Mathematical Statistics, 1965

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A gaussian vector is a vector such that every linear combination of its coefficients follows a gaussian distribution. If the coefficients of a vector follow a multivariate distribution, the vector should be gaussian. For the converse, each coefficient of a gaussian vector (as a trivial linear combination) should follow a gaussian distribution.