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A random vector x = [x1 , . . . , xN ]T RN×1 with expected value $\mu_x \operatorname{E}[x]$ and covariance matrix $C_x = \ldots$ is said to be (jointly) Gaussian, or multivariate normal, if
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i.e., if any linear combination of its components results in an univariate Gaussian random variable with the respective mean and variance.