## Elementary Probability for Applications

### Rick Durrett

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

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