John Tsitsiklis: Probabilistic Systems Analysis and Applied Probability (Fall 2013, MIT)

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source: MIT OpenCourseWare       Last updated on 2014年7月2日
MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013
This is a collection of 76 videos for MIT 6.041- 25 lectures videos (2010) and 51 recitation videos (2013). In the recitation videos MIT Teaching Assistants solve selected recitation and tutorial problems from the course.
View the complete course: http://ocw.mit.edu/6-041SCF13
Instructors: Qing He, Jimmy Li, Jagdish Ramakrishnan, Katie Szeto, and Kuang Xu
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu

1. Probability Models and Axioms 51:11
The Probability of the Difference of Two Events 5:55
Geniuses and Chocolates 8:43
Uniform Probabilities on a Square 9:17
2. Conditioning and Bayes' Rule 51:11
A Coin Tossing Puzzle 8:11
Conditional Probability Example 14:22
The Monty Hall Problem 15:59
3. Independence 46:30
A Random Walker 5:52
Communication over a Noisy Channel 19:53
Network Reliability 7:24
A Chess Tournament Problem 18:33
4. Counting 51:35
Rooks on a Chessboard 18:28
Hypergeometric Probabilities 5:49
5. Discrete Random Variables I 50:35
Sampling People on Buses 11:56
PMF of a Function of a Random Variable 15:26
6. Discrete Random Variables II 50:53
Flipping a Coin a Random Number of Times 8:43
Joint Probability Mass Function (PMF) Drill 1 17:37
The Coupon Collector Problem 7:15
7. Discrete Random Variables III 50:42
Joint Probability Mass Function (PMF) Drill 2 13:45
8. Continuous Random Variables 50:29
Calculating a Cumulative Distribution Function (CDF) 8:44
A Mixed Distribution Example 13:25
Mean & Variance of the Exponential 15:11
Normal Probability Calculation 5:25
9. Multiple Continuous Random Variables 50:51
Uniform Probabilities on a Triangle 22:58
Probability that Three Pieces Form a Triangle 12:30
The Absent Minded Professor 13:09
10. Continuous Bayes' Rule; Derived Distributions 48:53
Inferring a Discrete Random Variable from a Continuous Measurement 18:37
Inferring a Continuous Random Variable from a Discrete Measurement 11:35
A Derived Distribution Example 9:30
The Probability Distribution Function (PDF) of [X] 9:06
Ambulance Travel Time 6:47
11. Derived Distributions (ctd.); Covariance 51:55
The Difference of Two Independent Exponential Random Variables 6:12
The Sum of Discrete and Continuous Random Variables 5:37
12. Iterated Expectations 47:54
The Variance in the Stick Breaking Problem 11:30
Widgets and Crates 10:06
Using the Conditional Expectation and Variance 10:10
A Random Number of Coin Flips 17:19
A Coin with Random Bias 22:58
13. Bernoulli Process 50:58
Bernoulli Process Practice 8:22
14. Poisson Process I 52:44
Competing Exponentials 7:43
15. Poisson Process II 49:28
Random Incidence Under Erlang Arrivals 9:43
16. Markov Chains I 52:06
Setting Up a Markov Chain 10:36
Markov Chain Practice 1 11:42
17. Markov Chains II 51:25
18. Markov Chains III 51:50
Mean First Passage and Recurrence Times 9:27
19. Weak Law of Large Numbers 50:13
Convergence in Probability and in the Mean Part 1 13:37
Convergence in Probability and in the Mean Part 2 5:46
Convergence in Probability Example 7:37
20. Central Limit Theorem 51:23
Probabilty Bounds 10:46
Using the Central Limit Theorem 11:25
21. Bayesian Statistical Inference I 48:50
22. Bayesian Statistical Inference II 52:16
Inferring a Parameter of Uniform Part 1 24:52
Inferring a Parameter of Uniform Part 2 19:36
An Inference Example 27:51
23. Classical Statistical Inference I 49:32
24. Classical Inference II 51:50
25. Classical Inference III 52:07