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Probability

MIT 6.041, John Tsitsiklis · Math · Fall 2027 · Planned

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Lectures

1. Lecture 1: Probability Models and Axioms (51:10)
2. The Probability of the Difference of Two Events (5:55)
3. Geniuses and Chocolates (8:42)
4. Uniform Probabilities on a Square (9:16)
5. Lecture 2: Conditioning and Bayes' Rule (51:11)
6. A Coin Tossing Puzzle (8:10)
7. Conditional Probability Example (14:22)
8. The Monty Hall Problem (15:59)
9. Lecture 3: Independence (46:29)
10. A Random Walker (5:51)
11. Communication over a Noisy Channel (19:53)
12. Network Reliability (7:24)
13. A Chess Tournament Problem (18:33)
14. Lecture 4: Counting (51:34)
15. Rooks on a Chessboard (18:27)
16. Hypergeometric Probabilities (5:48)
17. Lecture 5: Discrete Random Variables I (50:34)
18. Sampling People on Buses (11:55)
19. PMF of a Function of a Random Variable (15:26)
20. Lecture 6: Discrete Random Variables II (50:52)
21. Flipping a Coin a Random Number of Times (8:43)
22. Joint Probability Mass Function (PMF) Drill 1 (17:37)
23. The Coupon Collector Problem (7:15)
24. Lecture 7: Discrete Random Variables III (50:41)
25. Joint Probability Mass Function (PMF) Drill 2 (13:45)
26. Lecture 8: Continuous Random Variables (50:28)
27. Calculating a Cumulative Distribution Function (CDF) (8:44)
28. A Mixed Distribution Example (13:24)
29. Mean & Variance of the Exponential (15:10)
30. Normal Probability Calculation (5:24)
31. Lecture 9: Multiple Continuous Random Variables (50:50)
32. Recitation: Uniform Probabilities on a Triangle (22:58)
33. Recitation: Probability that Three Pieces Form a Triangle (12:30)
34. Recitation: The Absent-Minded Professor (13:09)
35. Lecture 10: Continuous Bayes' Rule; Derived Distributions (48:52)
36. Recitation: Inferring a Discrete Variable from a Continuous Measurement (18:36)
37. Inferring a Continuous Random Variable from a Discrete Measurement (11:35)
38. Recitation: A Derived Distribution Example (9:30)
39. Recitation: The PDF of the Absolute Value of X (9:05)
40. Recitation: Ambulance Travel Time (6:47)
41. 11. Derived Distributions (ctd.); Covariance (51:54)
42. The Difference of Two Independent Exponential Random Variables (6:12)
43. The Sum of Discrete and Continuous Random Variables (5:37)
44. 12. Iterated Expectations (47:53)
45. The Variance in the Stick Breaking Problem (11:30)
46. Widgets and Crates (10:06)
47. Using the Conditional Expectation and Variance (10:10)
48. A Random Number of Coin Flips (17:19)
49. A Coin with Random Bias (22:58)
50. 13. Bernoulli Process (50:57)
51. Bernoulli Process Practice 1 (8:21)
52. Lecture 14: Poisson Process I (52:43)
53. Competing Exponentials (7:42)
54. Lecture 15: Poisson Process II (49:27)
55. Random Incidence Under Erlang Arrivals (9:43)
56. Lecture 16: Markov Chains I (52:05)
57. Setting Up a Markov Chain (10:36)
58. Markov Chain Practice 1 (11:41)
59. Lecture 17: Markov Chains II (51:24)
60. Lecture 18: Markov Chains III (51:49)
61. Mean First Passage and Recurrence Times (9:27)
62. Lecture 19: Weak Law of Large Numbers (50:12)
63. Convergence in Probability and in the Mean, Part 1 (13:36)
64. Convergence in Probability and in the Mean, Part 2 (5:45)
65. Convergence in Probability, Example (7:36)
66. Lecture 20: Central Limit Theorem (51:22)
67. Probability Bounds (10:45)
68. Using the Central Limit Theorem (11:24)
69. Lecture 21: Bayesian Statistical Inference I (48:49)
70. Lecture 22: Bayesian Statistical Inference II (52:15)
71. Inferring a Parameter of the Uniform Distribution, Part 1 (24:51)
72. Inferring a Parameter of the Uniform Distribution, Part 2 (19:35)
73. An Inference Example (27:50)
74. Lecture 23: Classical Statistical Inference I (49:31)
75. Lecture 24: Classical Inference II (51:49)
76. Lecture 25: Classical Inference III (52:06)

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