Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 4, pp. 880-884
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V. G. Mikhailov. The central limit theorem for the number of partial long duplications. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 4, pp. 880-884. http://geodesic.mathdoc.fr/item/TVP_1975_20_4_a16/
@article{TVP_1975_20_4_a16,
author = {V. G. Mikhailov},
title = {The central limit theorem for the number of partial long duplications},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {880--884},
year = {1975},
volume = {20},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1975_20_4_a16/}
}
TY - JOUR
AU - V. G. Mikhailov
TI - The central limit theorem for the number of partial long duplications
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1975
SP - 880
EP - 884
VL - 20
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1975_20_4_a16/
LA - ru
ID - TVP_1975_20_4_a16
ER -
%0 Journal Article
%A V. G. Mikhailov
%T The central limit theorem for the number of partial long duplications
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1975
%P 880-884
%V 20
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1975_20_4_a16/
%G ru
%F TVP_1975_20_4_a16
Let $X_1,X_2,\dots$ be a sequence of independent random variables, $X_i=1,2,\dots$. We prove the central limit theorem for the number of sets ($i_1,\dots,i_m$), $1\le i_1<\dots, such that the conditions $$ X_{i_1+k}=\dots=X_{i_m+k} $$ are satisfied for exactly $s-d$ values of $k\in\{0,\dots,s-1\}$.
