# Probabilistic Systems Analysis and Applied Probability (2013)

## by John Tsitsiklis, Qing He, Jimmy Li, Jagdish Ramakrishnan, Katie Szeto, Kuang Xu

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#### Description

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

Name | Description | Released | Price | ||
---|---|---|---|---|---|

1 | VideoLecture 1: Probability Models and Axioms | In this lecture, the professor discussed probability as a mathematical framework, probabilistic models, axioms of probability, and gave some simple examples. | 7/8/2015 | Free | View in iTunes |

2 | VideoThe Probability of the Difference of Two Events | -- | 7/7/2015 | Free | View in iTunes |

3 | VideoGeniuses and Chocolates | -- | 7/7/2015 | Free | View in iTunes |

4 | VideoUniform Probabilities on a Square | -- | 7/7/2015 | Free | View in iTunes |

5 | VideoLecture 2: Conditioning and Bayes' Rule | In this lecture, the professor discussed conditional probability, multiplication rule, total probability theorem, and Bayes' rule. | 7/8/2015 | Free | View in iTunes |

6 | VideoA Coin Tossing Puzzle | -- | 7/7/2015 | Free | View in iTunes |

7 | VideoConditional Probability Example | -- | 7/7/2015 | Free | View in iTunes |

8 | VideoThe Monty Hall Problem | -- | 7/7/2015 | Free | View in iTunes |

9 | VideoLecture 3: Independence | In this lecture, the professor discussed independence of two events, independence of a collection of events, and independence vs. pairwise independence. | 7/8/2015 | Free | View in iTunes |

10 | VideoA Random Walker | -- | 7/7/2015 | Free | View in iTunes |

11 | VideoCommunication over a Noisy Channel | -- | 7/7/2015 | Free | View in iTunes |

12 | VideoNetwork Reliability | -- | 7/7/2015 | Free | View in iTunes |

13 | VideoA Chess Tournament Problem | -- | 7/7/2015 | Free | View in iTunes |

14 | VideoLecture 4: Counting | In this lecture, the professor discussed principles of counting, permutations, combinations, partitions, and binomial probabilities. | 7/8/2015 | Free | View in iTunes |

15 | VideoRooks on a Chessboard | -- | 7/8/2015 | Free | View in iTunes |

16 | VideoHypergeometric Probabilities | -- | 7/7/2015 | Free | View in iTunes |

17 | VideoLecture 5: Discrete Random Variables I | In this lecture, the professor discussed random variables, probability mass function, expectation, and variance. | 7/8/2015 | Free | View in iTunes |

18 | VideoSampling People on Buses | -- | 7/7/2015 | Free | View in iTunes |

19 | VideoPMF of a Function of a Random Variable | -- | 7/7/2015 | Free | View in iTunes |

20 | VideoLecture 6: Discrete Random Variables II | In this lecture, the professor discussed conditional PMF, geometric PMF, total expectation theorem, and joint PMF of two random variables. | 7/8/2015 | Free | View in iTunes |

21 | VideoFlipping a Coin a Random Number of Times | -- | 7/7/2015 | Free | View in iTunes |

22 | VideoJoint Probability Mass Function (PMF) Drill 1 | -- | 7/7/2015 | Free | View in iTunes |

23 | VideoThe Coupon Collector Problem | -- | 7/7/2015 | Free | View in iTunes |

24 | VideoLecture 7: Discrete Random Variables III | In this lecture, the professor discussed multiple random variables, expectations, and binomial distribution. | 7/8/2015 | Free | View in iTunes |

25 | VideoJoint Probability Mass Function (PMF) Drill 2 | -- | 7/7/2015 | Free | View in iTunes |

26 | VideoLecture 8: Continuous Random Variables | In this lecture, the professor discussed probability density functions, cumulative distribution functions, and normal random variables. | 7/8/2015 | Free | View in iTunes |

27 | VideoCalculating a Cumulative Distribution Function (CDF) | -- | 7/7/2015 | Free | View in iTunes |

28 | VideoA Mixed Distribution Example | -- | 7/7/2015 | Free | View in iTunes |

29 | VideoMean & Variance of the Exponential | -- | 7/7/2015 | Free | View in iTunes |

30 | VideoNormal Probability Calculation | -- | 7/7/2015 | Free | View in iTunes |

31 | VideoLecture 9: Multiple Continuous Random Variables | In this lecture, the professor discussed multiple random variables: conditioning and independence. | 7/8/2015 | Free | View in iTunes |

32 | VideoUniform Probabilities on a Triangle | -- | 7/7/2015 | Free | View in iTunes |

33 | VideoProbability that Three Pieces Form a Triangle | -- | 7/8/2015 | Free | View in iTunes |

34 | VideoThe Absent Minded Professor | -- | 7/7/2015 | Free | View in iTunes |

35 | VideoLecture 10: Continuous Bayes' Rule; Derived Distributions | In this lecture, the professor discussed Bayes rule, Bayes variations, and derived distributions. | 7/8/2015 | Free | View in iTunes |

36 | VideoInferring a Discrete Random Variable from a Continuous Measurement | -- | 7/7/2015 | Free | View in iTunes |

37 | VideoInferring a Continuous Random Variable from a Discrete Measurement | -- | 7/7/2015 | Free | View in iTunes |

38 | VideoA Derived Distribution Example | -- | 7/7/2015 | Free | View in iTunes |

39 | VideoThe Probability Distribution Function (PDF) of [X] | -- | 7/7/2015 | Free | View in iTunes |

40 | VideoAmbulance Travel Time | -- | 7/7/2015 | Free | View in iTunes |

41 | VideoLecture 11: Derived Distributions (ctd | In this lecture, the professor discussed derived distributions, convolution, covariance and correlation. | 7/8/2015 | Free | View in iTunes |

42 | VideoThe Difference of Two Independent Exponential Random Variables | -- | 7/7/2015 | Free | View in iTunes |

43 | VideoThe Sum of Discrete and Continuous Random Variables | -- | 7/7/2015 | Free | View in iTunes |

44 | VideoLecture 12: Iterated Expectations | In this lecture, the professor discussed conditional expectation and sum of a random number of random variables. | 7/8/2015 | Free | View in iTunes |

45 | VideoThe Variance in the Stick Breaking Problem | -- | 7/7/2015 | Free | View in iTunes |

46 | VideoWidgets and Crates | -- | 7/7/2015 | Free | View in iTunes |

47 | VideoUsing the Conditional Expectation and Variance | -- | 7/7/2015 | Free | View in iTunes |

48 | VideoA Random Number of Coin Flips | -- | 7/7/2015 | Free | View in iTunes |

49 | VideoA Coin with Random Bias | -- | 7/7/2015 | Free | View in iTunes |

50 | VideoLecture 13: Bernoulli Process | In this lecture, the professor discussed Bernoulli process, random processes, basic properties of Bernoulli process, distribution of interarrival times, the time of the kth success, merging and splitting. | 7/8/2015 | Free | View in iTunes |

51 | VideoBernoulli Process Practice | -- | 7/7/2015 | Free | View in iTunes |

52 | VideoLecture 14: Poisson Process I | In this lecture, the professor discussed Poisson process, distribution of number of arrivals, and distribution of interarrival times. | 7/8/2015 | Free | View in iTunes |

53 | VideoCompeting Exponentials | -- | 7/7/2015 | Free | View in iTunes |

54 | VideoLecture 15: Poisson Process II | In this lecture, the professor discussed Poisson process, merging, splitting, and random incidence. | 7/8/2015 | Free | View in iTunes |

55 | VideoRandom Incidence Under Erlang Arrivals | -- | 7/7/2015 | Free | View in iTunes |

56 | VideoLecture 16: Markov Chains I | In this lecture, the professor discussed Markov process definition, n-step transition probabilities, and classification of states. | 7/8/2015 | Free | View in iTunes |

57 | VideoSetting Up a Markov Chain | -- | 7/7/2015 | Free | View in iTunes |

58 | VideoMarkov Chain Practice 1 | -- | 7/7/2015 | Free | View in iTunes |

59 | VideoLecture 17: Markov Chains II | In this lecture, the professor discussed Markov process, steady-state behavior, and birth-death processes. | 7/8/2015 | Free | View in iTunes |

60 | VideoLecture 18: Markov Chains III | In this lecture, the professor discussed Markov Processes, probability of blocked phone calls, absorption probabilities, and calculating expected time to absorption. | 7/8/2015 | Free | View in iTunes |

61 | VideoMean First Passage and Recurrence Times | -- | 7/7/2015 | Free | View in iTunes |

62 | VideoLecture 19: Weak Law of Large Numbers | In this lecture, the professor discussed limit theorems, Chebyshev's inequality, and convergence "in probability". | 7/8/2015 | Free | View in iTunes |

63 | VideoConvergence in Probability and in the Mean Part 1 | -- | 7/7/2015 | Free | View in iTunes |

64 | VideoConvergence in Probability and in the Mean Part 2 | -- | 7/7/2015 | Free | View in iTunes |

65 | VideoConvergence in Probability Example | -- | 7/7/2015 | Free | View in iTunes |

66 | VideoLecture 20: Central Limit Theorem | In this lecture, the professor discussed central limit theorem, Normal approximation, 1/2 correction for binomial approximation, and De Moivre–Laplace central limit theorem. | 7/8/2015 | Free | View in iTunes |

67 | VideoUsing the Central Limit Theorem | -- | 7/7/2015 | Free | View in iTunes |

68 | VideoProbabilty Bounds | -- | 7/7/2015 | Free | View in iTunes |

69 | VideoLecture 21: Bayesian Statistical Inference I | In this lecture, the professor discussed Bayesian statistical inference and inference models. | 7/8/2015 | Free | View in iTunes |

70 | VideoLecture 22: Bayesian Statistical Inference II | In this lecture, the professor discussed Bayesian statistical inference, least means squares, and linear LMS estimation. | 7/8/2015 | Free | View in iTunes |

71 | VideoInferring a Parameter of Uniform Part 1 | -- | 7/7/2015 | Free | View in iTunes |

72 | VideoInferring a Parameter of Uniform Part 2 | -- | 7/7/2015 | Free | View in iTunes |

73 | VideoAn Inference Example | -- | 7/7/2015 | Free | View in iTunes |

74 | VideoLecture 23: Classical Statistical Inference I | In this lecture, the professor discussed classical statistics, maximum likelihood (ML) estimation, and confidence intervals. | 7/8/2015 | Free | View in iTunes |

75 | VideoLecture 24: Classical Inference II | In this lecture, the professor discussed classical inference, Linear regression, and binary hypothesis testing. | 7/8/2015 | Free | View in iTunes |

76 | VideoLecture 25: Classical Inference III | In this lecture, the professor discussed classical inference, simple binary hypothesis testing, and composite hypotheses testing. | 7/8/2015 | Free | View in iTunes |

76 Items |

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