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Chapter 1. Basic Concepts 3/10/08
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 1/27/08
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 1/28/08
3.1. Definition
3.2. Two-stage experiments
3.3. Bayes formula
3.4. Exercises
Chapter 4. Markov Chains 2/11/08
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 3/26/08
5.1. Density and 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 3/21/08
6.1. Sums of independent random variables
6.2. Mean and variance of sums
6.3. Law of large numbers
6.4. Central limit theorem
6.5. Exercises
Chapter 7. Option pricing 4/22/08
7.1. Discrete time
7.2. Continuous time