Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 3, pp. 579-584
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G. D. Kartashov; A. N. Yavriyan. On an extremal problem in probability theory. Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 3, pp. 579-584. http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a21/
@article{TVP_1965_10_3_a21,
author = {G. D. Kartashov and A. N. Yavriyan},
title = {On an extremal problem in probability theory},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {579--584},
year = {1965},
volume = {10},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a21/}
}
TY - JOUR
AU - G. D. Kartashov
AU - A. N. Yavriyan
TI - On an extremal problem in probability theory
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1965
SP - 579
EP - 584
VL - 10
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a21/
LA - ru
ID - TVP_1965_10_3_a21
ER -
%0 Journal Article
%A G. D. Kartashov
%A A. N. Yavriyan
%T On an extremal problem in probability theory
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1965
%P 579-584
%V 10
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a21/
%G ru
%F TVP_1965_10_3_a21
The paper considers the problem of finding the absolute maximum and the absolute minimum of functional (1) where $x$ and $y$ are two dependend vector-valued random variables and $Q(y\mid x)$ is an unknown conditional distribution function. The problem is solved when $I_Q(x)$ is a monotone function of all the variables $x$ and the density functions of the random variables $x$ and $y$ are known.
