1 Probability questions
2 The law of large numbers and simulation
2.1 The law of large numbers for probabilities
2.2 Basic probability concepts
2.3 Expected value and the law of large numbers
2.4 The drunkard’s walk
2.5 The St. Petersburg paradox
2.6 Roulette and the law of large numbers
2.7 The Kelly betting system
2.8 Random-number generator
2.9 Simulating from probability distributions
2.10 Problems
3 Probabilities in everyday life
3.1 The birthday problem
3.2 The coupon collector’s problem
3.3 Craps
3.4 Gambling systems for roulette
3.5 The 1970 draft lottery
3.6 Bootstrap method
3.7 Problems
4 Rare events and lotteries
4.1 The binomial distribution
4.2 The Poisson distribution
4.3 The hypergeometric distribution
4.4 Problems
5 Probability and statistics
5.1 The normal curve
5.2 The concept of standard deviation
5.3 The square-root law
5.4 The central limit theorem
5.5 Graphical illustration of the central limit
theorem
5.6 Statistical applications
5.7 Confidence intervals for simulations
5.8 The central limit theorem and random walks
5.9 Falsified data and Benford’s law
5.10 The normal distribution strikes again
5.11 Statistics and probability theory
5.12 Problems
6 Chance trees and Bayes’ rule
6.1 The Monty Hall dilemma
6.2 The test paradox
6.3 Problems
PART TWO: ESSENTIALS OF PROBABILITY
7 Foundations of probability theory
7.1 Probabilistic foundations
7.2 Compound chance experiments
7.3 Some basic rules
8 Conditional probability and Bayes
8.1 Conditional probability
8.2 Bayes’ rule in odds form
8.3 Bayesian statistics
9 Basic rules for discrete random variables
9.1 Random variables
9.2 Expected value
9.3 Expected value of sums of random variables
9.4 Substitution rule and variance
9.5 Independence of random variables
9.6 Special discrete distributions
10 Continuous random variables
10.1 Concept of probability density
10.2 Important probability densities
10.3 Transformation of random variables
10.4 Failure rate function
11 Jointly distributed random variables
11.1 Joint probability densities
11.2 Marginal probability densities
11.3 Transformation of random variables
11.4 Covariance and correlation coefficient
12 Multivariate normal distribution
12.1 Bivariate normal distribution
12.2 Multivariate normal distribution
12.3 Multidimensional central limit theorem
12.4 The chi-square test
13 Conditional distributions
13.1 Conditional probability densities
13.2 Law of conditional probabilities
13.3 Law of conditional expectations
14 Generating functions
14.1 Generating functions
14.2 Moment-generating functions
15 Markov chains
15.1 Markov model
15.2 Transient analysis of Markov chains
15.3 Absorbing Markov chains
15.4 Long-run analysis of Markov chains
Good for the introduction purposes. BTW, this is the book I had reviewed recently and I'm not sure if they have published the second one of this. And one correction, in above post I said there were 14 chapters - there are 15.
