Two characteristic properties of normal distributions in the class $NH$

V. A. Romanovich, N. V. Lobaskina

Tomsk State University

Abstract: In this note are deduced two characterizations of normal distributions in the class $NH$ of probability distributions on a plane whose densities admit diagonal expansions in series of Hermite polynomials and the marginal distributions are standardized and normal.

UDC: 519.2

Received: 02.01.1975

 English version: Mathematical Notes, 1976, 20:1, 636–640

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