[1]An Introduction to Probability Theory - Geiss
目录是直接从PDF里复制出来粘贴的。清晰。
1 Probability spaces 7
1.1 Definition of -algebras . . . . . . . . . . . . . . . . . . . . . . 8
1.2 Probability measures . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 Examples of distributions . . . . . . . . . . . . . . . . . . . . 20
1.3.1 Binomial distribution with parameter 0 < p < 1 . . . . 20
1.3.2 Poisson distribution with parameter  > 0 . . . . . . . 21
1.3.3 Geometric distribution with parameter 0 < p < 1 . . . 21
1.3.4 Lebesgue measure and uniform distribution . . . . . . 21
1.3.5 Gaussian distribution on R with mean m 2 R and
variance 2 > 0 . . . . . . . . . . . . . . . . . . . . . . 22
1.3.6 Exponential distribution on R with parameter  > 0 . 22
1.3.7 Poisson’s Theorem . . . . . . . . . . . . . . . . . . . . 24
1.4 A set which is not a Borel set . . . . . . . . . . . . . . . . . . 25
2 Random variables 29
2.1 Random variables . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 Measurable maps . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3 Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3 Integration 39
3.1 Definition of the expected value . . . . . . . . . . . . . . . . . 39
3.2 Basic properties of the expected value . . . . . . . . . . . . . . 42
3.3 Connections to the Riemann-integral . . . . . . . . . . . . . . 48
3.4 Change of variables in the expected value . . . . . . . . . . . . 49
3.5 Fubini’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.6 Some inequalities . . . . . . . . . . . . . . . . . . . . . . . . . 58
4 Modes of convergence 63
4.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Some applications . . . . . . . . . . . . . . . . . . . . . . . . . 64


[3]Applied Probability - Lange K.
Contents（部分目录，从PDF直接复制出来的）总共379页，全15章，清晰。
Preface to the Second Edition vii
Preface to the First Edition ix
0.1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
1 Basic Principles of Population Genetics 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Genetics Background . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Hardy-Weinberg Equilibrium . . . . . . . . . . . . . . . . . 4
1.4 Linkage Equilibrium . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.6 Balance Between Mutation and Selection . . . . . . . . . . 12
1.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 Counting Methods and the EM Algorithm 21
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Gene Counting . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 Description of the EM Algorithm . . . . . . . . . . . . . . . 23
2.4 Ascent Property of the EM Algorithm . . . . . . . . . . . . 24
2.5 Allele Frequency Estimation by the EM Algorithm . . . . . 26
2.6 Classical Segregation Analysis by the EM Algorithm . . . . 27
2.7 Binding Domain Identification . . . . . . . . . . . . . . . . . 31
2.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3 Newton’s Method and Scoring 39
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 Newton’s Method . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3 Scoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4 Application to the Design of Linkage Experiments . . . . . 43
3.5 Quasi-Newton Methods . . . . . . . . . . . . . . . . . . . . 45
3.6 The Dirichlet Distribution . . . . . . . . . . . . . . . . . . . 47
3.7 Empirical Bayes Estimation of Allele Frequencies . . . . . . 48
3.8 Empirical Bayes Estimation of Haplotype Frequencies . . . 51
3.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
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