Discrete Probability

1 Introduction. - 2 Counting. - 2. 1 order counts with replacement. - 2. 2 order counts without replacement. - 2. 3 order does not count without replacement. - 2. 4 order does not count with replacement. - 3 Independence and Conditional Probability. - 3. 1 Independence. - 3. 2 Bernoulli Trials. - 3. 3 The Most Likely Number of Successes. - 3. 4 Conditional Probability. - 4 Random Variables. - 4. 1 Expected Value and Variance. - 4. 2 Computation of Expected Value and Variance. - 5 More About Random Variables. - 5. 1 The Law of Large Numbers. - 5. 2 Conditional Probability. - 5. 3 Computation of Variance. - 6 Approximating Probabilities. - 6. 1 The Poisson Distribution. - 6. 2 Stirling's Formula. - 6. 3 The Normal Distribution. - 7 Generating Functions. - 8 Random Walks. - 8. 1 The Probability Peter Wins. - 8. 2 The Duration of Play. - 9 Markov Chains. - 9. 1 What Is a Markov Chain?. - 9. 2 Where Do We Get and How Often?. - 9. 3 How Long Does It Take?. - 9. 4 What Happens in the Long Run?. - Table of Important Distributions. - Answers. Language: English