Index
An infinitel y often , 89 , 9 4
arcsine la w
generalized form , 133
proof, 71-73
statement, 6 0
asymptotic notation , 2 6
asymptotic probability , 8 3
base b representation, 86—8 8
Bernoulli distribution , 16
Bernstein polynomial , 21-22
Bienayme Chebyshe v inequality , 9
binomial coefficients , 15
binomial distribution , 16
binomial theorem , 16
Boolean algebra , 7 9
Borel-Cantelli lemm a
first, 89-9 0
second, 94-9 6
central limi t theore m
applications, 33-3 6
generalized form , 132
proof, 43-4 4
statement, 3 0
with variabl e bounds , 4 8
characteristic function , 4 , 9 0
de Moivre-Laplac e theorem , 39—4 1
distribution o f a rando m variable , 7
empirical probability , 2 0
event
almost sure , 7 9
definition of , 3
finite type , 78 ,
independent s , 80
negligible, 79-80 , 81-82
expected value , 7-9 , 14, 16-17, 9 1
experiment
elementary, 3- 6
finite sequenc e o f s , 5—6
infinite sequenc e o f s , 7 8
experimental probability , 2 0
Gaussian curve , 30-3 1
Gaussian distribution , 29-3 2
Hardy an d Littlewood' s estimate , 100
Hausdorff's estimate , 9 9
independent
events, 11-12
random variables , 12-14, 9 1
sequence o f events , 5-6 , 7 8
inequality
Bienayme-Chebyshev, 9
Markov's, 8
maximal, 101
invariance unde r shifting , 7 9
iterated logarithm , la w o f th e
generalized form , 134
proof, 103
statement , 100
large deviation s estimat e
generalized form , 132
proof, 24-2 5
statement , 2 3
large numbers , la w o f
generalized form , 93 , 131-132
strong, 8 2
149
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