MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013 (English)

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Lecture 1: 1. Probability Models and Axioms

Lecture 2: The Probability of the Difference of Two Events

Lecture 3: Geniuses and Chocolates

Lecture 4: Uniform Probabilities on a Square

Lecture 5: 2. Conditioning and Bayes' Rule

Lecture 6: A Coin Tossing Puzzle

Lecture 7: Conditional Probability Example

Lecture 8: The Monty Hall Problem

Lecture 9: 3. Independence

Lecture 10: A Random Walker

Lecture 11: Communication over a Noisy Channel

Lecture 12: Network Reliability

Lecture 13: A Chess Tournament Problem

Lecture 14: 4. Counting

Lecture 15: Rooks on a Chessboard

Lecture 16: Hypergeometric Probabilities

Lecture 17: 5. Discrete Random Variables I

Lecture 18: Sampling People on Buses

Lecture 19: PMF of a Function of a Random Variable

Lecture 20: 6. Discrete Random Variables II

Lecture 21: Flipping a Coin a Random Number of Times

Lecture 22: Joint Probability Mass Function (PMF) Drill 1

Lecture 23: The Coupon Collector Problem

Lecture 24: 7. Discrete Random Variables III

Lecture 25: Joint Probability Mass Function (PMF) Drill 2

Lecture 26: 8. Continuous Random Variables

Lecture 27: Calculating a Cumulative Distribution Function (CDF)

Lecture 28: A Mixed Distribution Example

Lecture 29: Mean & Variance of the Exponential

Lecture 30: Normal Probability Calculation

Lecture 31: 9. Multiple Continuous Random Variables

Lecture 32: Uniform Probabilities on a Triangle

Lecture 33: Probability that Three Pieces Form a Triangle

Lecture 34: The Absent Minded Professor

Lecture 35: 10. Continuous Bayes' Rule; Derived Distributions

Lecture 36: Inferring a Discrete Random Variable from a Continuous Measurement

Lecture 37: Inferring a Continuous Random Variable from a Discrete Measurement

Lecture 38: A Derived Distribution Example

Lecture 39: The Probability Distribution Function (PDF) of [X]

Lecture 40: Ambulance Travel Time

Lecture 41: 11. Derived Distributions (ctd.); Covariance

Lecture 42: The Difference of Two Independent Exponential Random Variables

Lecture 43: The Sum of Discrete and Continuous Random Variables

Lecture 44: 12. Iterated Expectations

Lecture 45: The Variance in the Stick Breaking Problem

Lecture 46: Widgets and Crates

Lecture 47: Using the Conditional Expectation and Variance

Lecture 48: A Random Number of Coin Flips

Lecture 49: A Coin with Random Bias

Lecture 50: 13. Bernoulli Process

Lecture 51: Bernoulli Process Practice

Lecture 52: 14. Poisson Process I

Lecture 53: Competing Exponentials

Lecture 54: 15. Poisson Process II

Lecture 55: Random Incidence Under Erlang Arrivals

Lecture 56: 16. Markov Chains I

Lecture 57: Setting Up a Markov Chain

Lecture 58: Markov Chain Practice 1

Lecture 59: 17. Markov Chains II

Lecture 60: 18. Markov Chains III

Lecture 61: Mean First Passage and Recurrence Times

Lecture 62: 19. Weak Law of Large Numbers

Lecture 63: Convergence in Probability and in the Mean Part 1

Lecture 64: Convergence in Probability and in the Mean Part 2

Lecture 65: Convergence in Probability Example

Lecture 66: 20. Central Limit Theorem

Lecture 67: Probabilty Bounds

Lecture 68: Using the Central Limit Theorem

Lecture 69: 21. Bayesian Statistical Inference I

Lecture 70: 22. Bayesian Statistical Inference II

Lecture 71: Inferring a Parameter of Uniform Part 1

Lecture 72: Inferring a Parameter of Uniform Part 2

Lecture 73: An Inference Example

Lecture 74: 23. Classical Statistical Inference I

Lecture 75: 24. Classical Inference II

Lecture 76: 25. Classical Inference III