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2. Conditioning and Bayes' Rule
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Classroom Contents
Probabilistic Systems Analysis and Applied Probability
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- 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
