1 1. Probability Models and Axioms 2 The Probability of the Difference of Two Events 3 Geniuses and Chocolates 4 Uniform Probabilities on a Square 5 2. Conditioning and Bayes' Rule 6 A Coin Tossing Puzzle 7 Conditional Probability Example 8 The Monty Hall Problem 9 3. Independence 10 A Random Walker 11 Communication over a Noisy Channel 12 Network Reliability 13 A Chess Tournament Problem 14 4. Counting 15 Rooks on a Chessboard 16 Hypergeometric Probabilities 17 5. Discrete Random Variables I 18 Sampling People on Buses 19 PMF of a Function of a Random Variable 20 6. Discrete Random Variables II 21 Flipping a Coin a Random Number of Times 22 Joint Probability Mass Function (PMF) Drill 1 23 The Coupon Collector Problem 24 7. Discrete Random Variables III 25 Joint Probability Mass Function (PMF) Drill 2 26 8. Continuous Random Variables 27 Calculating a Cumulative Distribution Function (CDF) 28 A Mixed Distribution Example 29 Mean & Variance of the Exponential 30 Normal Probability Calculation 31 9. Multiple Continuous Random Variables 32 Uniform Probabilities on a Triangle 33 Probability that Three Pieces Form a Triangle 34 The Absent Minded Professor 35 10. Continuous Bayes' Rule; Derived Distributions 36 Inferring a Discrete Random Variable from a Continuous Measurement 37 Inferring a Continuous Random Variable from a Discrete Measurement 38 A Derived Distribution Example 39 The Probability Distribution Function (PDF) of [X] 40 Ambulance Travel Time 41 11. Derived Distributions (ctd.); Covariance 42 The Difference of Two Independent Exponential Random Variables 43 The Sum of Discrete and Continuous Random Variables 44 12. Iterated Expectations 45 The Variance in the Stick Breaking Problem 46 Widgets and Crates 47 Using the Conditional Expectation and Variance 48 A Random Number of Coin Flips 49 A Coin with Random Bias 50 13. Bernoulli Process 51 Bernoulli Process Practice 52 14. Poisson Process I 53 Competing Exponentials 54 15. Poisson Process II 55 Random Incidence Under Erlang Arrivals 56 16. Markov Chains I 57 Setting Up a Markov Chain 58 Markov Chain Practice 1 59 17. Markov Chains II 60 18. Markov Chains III 61 Mean First Passage and Recurrence Times 62 19. Weak Law of Large Numbers 63 Convergence in Probability and in the Mean Part 1 64 Convergence in Probability and in the Mean Part 2 65 Convergence in Probability Example 66 20. Central Limit Theorem 67 Probabilty Bounds 68 Using the Central Limit Theorem 69 21. Bayesian Statistical Inference I 70 22. Bayesian Statistical Inference II 71 Inferring a Parameter of Uniform Part 1 72 Inferring a Parameter of Uniform Part 2 73 An Inference Example 74 23. Classical Statistical Inference I 75 24. Classical Inference II 76 25. Classical Inference III