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.