## Elementary Probability for Applications

### Rick Durrett

Chapter 1. Basic Concepts

1.1. Outcomes, Events, Probability
1.2. Flipping coins, the World Series
1.3. Independence
1.4. Distributions
1.5. Expected Value
1.6. Moments, Variance
1.7. Exercises

Chapter 2. Combinatorial Probability

2.1. Permutations and combinations
2.2. Binomial and multinomial distributions
2.3. Poisson approximation
2.4. Card games and other urn problems
2.5. Probabilities of unions, Joe DiMaggio's streak
2.6. Blackjack
2.7. Exercises

Chapter 3. Conditional Probability

3.1. Definition
3.2. Two-stage experiments
3.3. Bayes formula
3.4. Joint distributions
3.5. Exercises

Chapter 4. Markov Chains

4.1. Definitions and examples
4.2. Multistep transition probabilities
4.3. Stationary distributions
4.4. Limit behavior
4.5. Gambler's ruin
4.6. Absrobing chains
4.7. Exercises

Chapter 5. Continuous Distributions

5.1. Density functions
5.2. Distribution functions
5.2. Functions of random variables
5.3. Joint distributions
5.4. Marginal and condtitional distributions
5.5. Exercises

Chapter 6. Limit Theorems

6.1. Sums of independent random variables
6.2. Mean and variance of sums
6.3. Laws of large numbers
6.4. Normal distribution
6.5. Central limit theorem
6.6. Applications to statistics
6.7. Exercises

Chapter 7. Option pricing

7.1. Discrete time
7.2. Continuous time