SUMMARY Let y1, y2, · · ·*** be pairwise independent quadratic expressions in x, not necessarily homogeneous, where x has a multinormal distribution. Then y1, y2, …*** are also mutually independent. Various conditions for independence are given. In the Appendix, it is shown that x is a linear transformation of a vector z, where z has a spherically symmetric distribution, and where the y’s depend on disjoint subsets of the components of z.
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Good et al. (1963) studied this question.
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