Book has been published by Cambridge U. Press in 2009
Beta test version of third edtion:
Version 2.4, April 2021
Chapter 1. Combinatorial Probability
1.1. Basic definitions
1.2. Permutations and combinations
1.3. Flipping coins, the World Series, Birthdays
1.3. Poisson approximation
1.4. Random variables, Expected value
1.5. Card games and other urn problems
1.6. Exercises
Chapter 2. Independence
2.1. Conditional Probability
2.2. Geometric, Binomial, and Multinomial
2.3. Poisson approximation to the Binomial
2.4. Probabilities of unions
2.5. Exercises
Cahpter 3. Random Variables and their Distributions
3.1. Distributions
3.2. Distribution functions
3.3. Means and medians
3.4. Functions of random variables
3.5. Joint distributions
3.6. Exercises
Chapter 4. Limit theorems
4.1. Moments, variance
4.2. Sums of independent random variables
4.3. Variance of sums of independent random variables
4.4. Laws of large numbers
4.5. Central limit theorem
4.6. Confidence intervals for proportions
4.7. Exercises
Chapter 5. Conditional Probability
5.1. The multiplication rule
5.2. Two-stage experiments
5.3. Bayes formula
5.4. Exercises
Chapter 6. Markov Chains
6.1. Definitions and examples
6.2. Multistep transition probabilities
6.3. Stationary distributions
6.4. Limit behavior
6.5. Chains with absorbing states
6.6. Exercises