Reading assignments are from the course textbook:

Bertsekas, Dimitri, and John Tsitsiklis. *Introduction to Probability*. 2nd ed. Athena Scientific, 2008. ISBN: 978188652923.

LEC # | TOPICS | READINGS |
---|---|---|

1 | Probability models and axioms | Sections 1.1–1.2 |

2 | Conditioning and Bayes’ rule | Sections 1.3–1.4 |

3 | Independence | Section 1.5 |

4 | Counting | Section 1.6 |

5 | Discrete random variables; probability mass functions; expectations | Sections 2.1–2.4 |

6 | Discrete random variable examples; joint PMFs | Sections 2.4–2.5 |

7 | Multiple discrete random variables: expectations, conditioning, independence | Sections 2.6–2.7 |

8 | Continuous random variables | Sections 3.1–3.3 |

9 | Multiple continuous random variables | Sections 3.4–3.5 |

10 | Continuous Bayes rule; derived distributions | Sections 3.6; 4.1 |

11 | Derived distributions; convolution; covariance and correlation | Sections 4.1–4.2 |

12 | Iterated expectations; sum of a random number of random variables | Sections 4.3; 4.5 |

13 | Bernoulli process | Section 6.1 |

14 | Poisson process – I | Section 6.2 |

15 | Poisson process – II | Section 6.2 |

16 | Markov chains – I | Sections 7.1–7.2 |

17 | Markov chains – II | Section 7.3 |

18 | Markov chains – III | Section 7.3 |

19 | Weak law of large numbers | Sections 5.1–5.3 |

20 | Central limit theorem | Section 5.4 |

21 | Bayesian statistical inference – I | Sections 8.1–8.2 |

22 | Bayesian statistical inference – II | Sections 8.3–8.4 |

23 | Classical statistical inference – I | Section 9.1 |

24 | Classical inference – II | Sections 9.1–9.4 |

25 | Classical inference – III; course overview | Sections 9.1–9.4 |