# Probability and Random Processes

Fall 2021

Shyam Parekh

TuTh 5-6:30 PM, 2060 VLSB

Office Hours: WF 10-11am (v)

## Announcements

- Welcome to EECS 126! Please read the course info, join Piazza, and join Gradescope (code 74PB3B).
- Please note this is an in-person class with no recorded lectures or discussions, and in-person exams. There will, however, be a few virtual office hours and discussions. See calendar for the schedule.
- Here’s an anonymous feedback form for you to provide any suggestions to help us improve the class.

## Lecture Schedule

Readings refer to Walrand’s *Probability in Electrical Engineering and Computer Science*. Additionally, these Jupyter Notebooks provide extra reinforcement for the textbook.
Online notes will serve as optional supplemental readings, and will not directly correspond to
the lectures or textbook (see content).
The B&T textbook may also be useful, but is not the primary textbook.

Schedule is subject to some changes.

Date | Topics | Readings |
---|---|---|

08/26 | Elementary Probability: Symmetry, Expectation, Conditioning | Appendix A.1-A.5 |

08/31 | Elementary Probability: Bounds, Law of Large Numbers | Appendix A.6-A.9 |

09/02 | Basic Probability: Probability Space, RVs, Borel-Cantelli | Appendix B.1 |

09/07 | Basic Probability: Bayes Rule, Conditional RVs | Appendix B.2-B.3 |

09/09 | Basic Probability: Discrete RVs, Joint RVs, Independence | Appendix B.4-B.5 |

09/14 | Basic Probability: Continuous RVs, PageRank: Discrete Time Markov Chains, Big Theorem |
Appendix B.6-B.7 Section 1.1-1.3 Markov Chains |

09/16 | PageRank: Big Theorem | Section 1.3-1.4, 2.5 |

09/21 | PageRank: Big Theorem, Hitting Time, Convergence, Strong Law of Large Numbers | Section 1.5, 2.1-2.4 |

09/23 | No Lecture (Midterm 1) | |

09/28 | PageRank: Convergence, SLLN; Multiplexing: Gaussian RVs |
Convergence Section 3 |

09/30 | Multiplexing: Central Limit Theorem, Confidence Intervals | Section 3 |

10/05 | Multiplexing: Characteristic Functions | Section 4 |

10/07 | Networks: Queuing, Poisson Processes | Section 5 Random Graphs |

10/12 | Networks: Continuous Time Markov Chains | Section 6.1-6.2 CTMCS |

10/14 | Networks: CTMC Uniformization, Stationary Distribution | Section 6.3-6.4 |

10/19 | Networks: Product-Form Networks | |

10/21 | Networks: Wrap-up | |

10/26 | Digital Link: Introduction to Entropy | Section 7.1-7.5 Information Theory |

10/28 | Digital Link: Huffman Codes and BSE Channel Capacity | Section 7.1-7.5 Information Theory |

11/02 | Digital Link: MAP and MLE | |

11/04 | No Lecture (Midterm 2) | |

11/09 | Digital Link: Hypothesis Testing, ROC, Neyman-Pearson Theorem | Section 7.6, Section 8.1-8.2 Hypothesis Testing |

11/11 | No Lecture (Veteran’s Day) | |

11/16 | Digital Link: Jointly Gaussian RVs | Section 8.3-8.4 |

11/18 | Tracking: LLSE | Section 9.1-9.5 Hilbert space of RVs |

11/23 | Tracking: MMSE | Section 9.6-9.8 |

11/25 | No Lecture (Thanksgiving Break) | |

11/30 | Tracking: Kalman Filtering | Section 10.2-10.4 Kalman Filter |

12/02 | Review |