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Biometrika 1972 59(2):492-494; doi:10.1093/biomet/59.2.492
© 1972 by Biometrika Trust
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MISCELLANEA

On random sequences with spherical symmetry

J. F. C. KINGMAN

University of Oxford

An infinite sequence of random variables, any finite sample from which has a spherically symmetric joint distribution, is shown to have the property that, conditional on a further random variable V, the variables are independent with the same normal distribution N(0, V).

Key Words: Exchangeable • Spherical symmetry • Conditional independence • Normal distribution


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