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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
260 Combinatorics of Permutations, Second Edition
f
F
Normal Density Normal Distributio
n
FIGURE 6.12
Normal density and normal distribution.
and σ =1,andZ has normal distribution, then we say that Z has standard
normal distribution.
Let X
n
be a random variable, and let a
n
(k) be a triangular array of non-
negative real numbers, n =1, 2, ···,and0 k m(n)sothat
P [X
n
= k]=p
n
(k)=
a
n
(k)
m(n)
i=0
a
n
(i)
.
Set g
n
(x)=
m(n)
k=0
p
n
(k)x
k
.Inotherwords,g
n
(x) is a generating function
satisfying g
n
(1) = 1. Such generating functions are sometimes called proba-
bility generating functions.
Let us introduce the following notation that is standard in most probability
texts.
Let
¯
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Publisher Resources

ISBN: 9781439850527