# Probabilistic Systems Analysis and Applied Probability (2013)

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

To listen to an audio podcast, mouse over the title and click Play. Open iTunes to download and subscribe to iTunes U collections.

#### 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 |

- Free
- Category: Computer Science
- Language: English
- http://ocw.mit.edu; Creative Commons Attribution-NonCommercial-ShareAlike 3.0; http://ocw.mit.edu/terms

Discover and share

new apps.

Follow us on @AppStore.

Discover and share new music, movies, TV, books, and more.

Follow us @iTunes and discover

new iTunes Radio Stations

and the music we love.