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Combinatorics of Permutations, 2nd Edition
book

Combinatorics of Permutations, 2nd Edition

by Miklos Bona
April 2016
Intermediate to advanced content levelIntermediate to advanced
478 pages
14h 44m
English
Chapman and Hall/CRC
Content preview from Combinatorics of Permutations, 2nd Edition
Mean and Insensitive. Random Permutations. 255
as the choice of i and j is clearly insignificant.
The variables X
i,j
, or in general, variables taking values 0 and 1 depending
on the occurrence of an event, are called indicator random variables, and are
often very useful.
The following theorem is a not very subtle, but very general, tool in proving
that it is unlikely that a variable is larger than a multiple of its expectation.
(We will state the theorem in a special case that is relevant in our combina-
torial applications, but a more general treatment is possible.)
THEOREM 6.28
[Markov’s Inequality] Let X be any nonnegative random variable that has
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Publisher Resources

ISBN: 9781439850527