文档介绍：D
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Kolmogor
v Cramer
Bore
Lev
Keynes Feller
Co9-e9t0
uO uHn wOUoTH EDITION xi
PoOLOGUn TO INToODUCTION TO
MhTHEMhuICAL xiii
1Snu 1
Bample sets R
O´erations with sets 3
Various relations 7
Indicator R3
Exercises R7
2 roOBABILITY 20
Examples of ´robability 20
Definition and illustrations 24
Deductions froP the axioms 3R
Inde´endent events 35
Arithmetica’ density 39
Exercises 42
3cOUNuING 46
Fundamenta’ rule 46
Diverse wqys of sampling 49
Allocation models; binomia’ coefficients 55
How to solve it 62
Exercises 70
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vii2 Co´’e´t(
4 oANDOM VARIABLES 74
What is q randoP variable? 74
How do randoP e about? 78
Distribution qnd ex´ectation 84
Integer-valued randoP variables 90
RandoP variables with densities 95
Genera’ case 105
Exercises R09
APPENDIX 1: BOREL wIELDS hND GENERAL
RANDOM VhRIABLES 115
5CONDITIONING AND 117
Examples of conditioning 117
Basic forPulas 122
Bequentia’ sampling 13R
P´olyq’s urn scheme 136
Inde´endence qnd relevqnce 14R
ica’ models 152
Exercises 157
6 MEAN, VhRIANCE, hND TRANSwORMS 164
Basic pro´erties of ex´ectation 164
The density case 169
Multiplication theorem; variance qnd covqriance 173
Multinomia’ distribution 180
Generating function and the like 187
Exercises 195
7 rOISSON hND NORMAL DISTRIBUTIONS 203
Models for Poisson distribution 203
Poisson ´rocess 21R
FroP binomia’ to norma’ 222
Norma’ distribution 229
Centra’ limit theoreP 233
Lqw of large nuPbers 239
Exercises 246
APPENDIX 2: STIRLING’S wORMULh hND
Dn MOIVRE–LAPLhCE’S THEOREM 251
Co´’e´t( i3
8 woOM oANDOM WALKS TO MARKOV CHAINS 254
Problems of the wqnderer or gaPbler 254
Limiting schemes 26R
Transition ´robabilities 266
Basic structure of Markov chains 275
Further developments 284
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