# Probabilistic Systems Analysis and Applied Probability

## by John Tsitsiklis

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#### Description

Video Lectures from 6.041 Probabilistic Systems Analysis and Applied Probability, Fall 2010

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. | 11/9/12 | Free | View In iTunes |

2 | VideoLecture 2: Conditioning and Bayes' Rule | In this lecture, the professor discussed conditional probability, multiplication rule, total probability theorem, and Bayes' rule. | 11/9/12 | Free | View In iTunes |

3 | VideoLecture 3: Independence | In this lecture, the professor discussed independence of two events, independence of a collection of events, and independence vs. pairwise independence. | 11/9/12 | Free | View In iTunes |

4 | VideoLecture 4: Counting | In this lecture, the professor discussed principles of counting, permutations, combinations, partitions, and binomial probabilities. | 11/9/12 | Free | View In iTunes |

5 | VideoLecture 5: Discrete Random Variables I | In this lecture, the professor discussed random variables, probability mass function, expectation, and variance. | 11/9/12 | Free | View In iTunes |

6 | 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. | 11/9/12 | Free | View In iTunes |

7 | VideoLecture 7: Discrete Random Variables III | In this lecture, the professor discussed multiple random variables, expectations, and binomial distribution. | 11/9/12 | Free | View In iTunes |

8 | VideoLecture 8: Continuous Random Variables | In this lecture, the professor discussed probability density functions, cumulative distribution functions, and normal random variables. | 11/9/12 | Free | View In iTunes |

9 | VideoLecture 9: Multiple Continuous Random Variables | In this lecture, the professor discussed multiple random variables: conditioning and independence. | 11/9/12 | Free | View In iTunes |

10 | VideoLecture 10: Continuous Bayes' Rule; Derived Distributions | In this lecture, the professor discussed Bayes rule, Bayes variations, and derived distributions. | 11/9/12 | Free | View In iTunes |

11 | VideoLecture 11: Derived Distributions (ctd.); Covariance | In this lecture, the professor discussed derived distributions, convolution, covariance and correlation. | 11/9/12 | Free | View In iTunes |

12 | VideoLecture 12: Iterated Expectations | In this lecture, the professor discussed conditional expectation and sum of a random number of random variables. | 11/9/12 | Free | View In iTunes |

13 | 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. | 11/9/12 | Free | View In iTunes |

14 | VideoLecture 14: Poisson Process I | In this lecture, the professor discussed Poisson process, distribution of number of arrivals, and distribution of interarrival times. | 11/9/12 | Free | View In iTunes |

15 | VideoLecture 15: Poisson Process II | In this lecture, the professor discussed Poisson process, merging, splitting, and random incidence. | 11/9/12 | Free | View In iTunes |

16 | VideoLecture 16: Markov Chains I | In this lecture, the professor discussed Markov process definition, n-step transition probabilities, and classification of states. | 11/9/12 | Free | View In iTunes |

17 | VideoLecture 17: Markov Chains II | In this lecture, the professor discussed Markov process, steady-state behavior, and birth-death processes. | 11/9/12 | Free | View In iTunes |

18 | 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. | 11/9/12 | Free | View In iTunes |

19 | VideoLecture 19: Weak Law of Large Numbers | In this lecture, the professor discussed limit theorems, Chebyshev's inequality, and convergence "in probability". | 11/9/12 | Free | View In iTunes |

20 | 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. | 11/9/12 | Free | View In iTunes |

21 | VideoLecture 21: Bayesian Statistical Inference I | In this lecture, the professor discussed Bayesian statistical inference and inference models. | 11/9/12 | Free | View In iTunes |

22 | VideoLecture 22: Bayesian Statistical Inference II | In this lecture, the professor discussed Bayesian statistical inference, least means squares, and linear LMS estimation. | 11/9/12 | Free | View In iTunes |

23 | VideoLecture 23: Classical Statistical Inference I | In this lecture, the professor discussed classical statistics, maximum likelihood (ML) estimation, and confidence intervals. | 11/9/12 | Free | View In iTunes |

24 | VideoLecture 24: Classical Inference II | In this lecture, the professor discussed classical inference, Linear regression, and binary hypothesis testing. | 11/9/12 | Free | View In iTunes |

25 | VideoLecture 25: Classical Inference III | In this lecture, the professor discussed classical inference, simple binary hypothesis testing, and composite hypotheses testing. | 11/9/12 | Free | View In iTunes |

25 Items |

#### Customer Reviews

##### Excellent

This is an excellent course. I am preparing for an exam in May 2013. This resource has proved to be a life saver. It's comprehensive, easy to understand and rigorous. Thank you so much OCW and professor John.

##### Very Good

He explains things well.

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