Rotational Symmetry of Multivariate Uncorrelated Standard Normal Distribution

distance to tangential plane

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rotation of the radial and tangential planes

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Rotational symmetry is a key property of the multivariate uncorrelated standard normal distribution. The top part of this Demonstration displays the contour and the 3D plots of a bivariate uncorrelated standard normal distribution. Both plots are intersected by two vertical planes or half-spaces. The radial plane runs through the origin and the tangential plane is perpendicular to it at a variable distance. The bottom parts display the density profiles created by the intersections. These profiles are standard normals up to a normalizing constant.