# Electrical Engineering 126: Probability & Random Processes

## Announcements

- (12/2) Homework 11 solutions have been released. Homework 11 self-grades are due Monday, 12/4, 5 PM. Lab 3 solutions have been released. Lab 3 self-grades are due Monday, 12/4, 5 PM. The Final Review worksheet has been released. Sinho and Avishek will be in Cory 521 on Wednesday, 12/6, 2-4 PM, to questions.
- (11/27) Discussion 14 has been uploaded.
- (11/22) Homework 11 has been released; it is due Friday, 12/1, 9 AM.
- (11/21) Discussion 13 has been uploaded.
- (11/16) Homework 10 solutions have been released. Homework 10 self-grades are due Monday, 11/20, 5 PM.
- (11/15) Note on LQG has been posted.
- (11/13) Discussion 12 has been uploaded.
- (11/10) Homework 9 solutions have been released. Homework 9 self-grades are due Monday, 11/13, 5 PM. Homework 10 has been released; it is due Thursday, 11/16. Lab 3 has been released. It is due on Thursday, 11/30, 5 PM.
- (11/6) Discussion 11 has been uploaded.
- (11/3) Homework 8 solutions have been released. Homework 8 self-grades are due Monday, 11/6, 5 PM.
- (11/2) Homework 9 has been released; it is due Thursday, 11/9. Lab 2 solutions have been released. Lab 2 self-grades are due Monday, 11/6, 5 PM.
- (10/30) Discussion 10 has been uploaded.
- (10/28) Homework 8 has been released; it is due Thursday, 11/2.
- (10/23) Discussion 9 has been uploaded.
- (10/19) Homework 7 solutions have been released. Homework 7 self-grades are due Monday, 10/23, 5 PM. Lab 2 has been released. It is due on Thursday, 11/2, 9 AM. The Midterm 2 review session will be on Sunday, 10/22, 3-5 PM, 540AB Cory.
- (10/16) Discussion 8 has been uploaded.
- (10/13) Homework 6 solutions have been released. Homework 6 self-grades are due Monday, 10/16, 5 PM. Homework 7 has been released; it is due Thursday, 10/19.
- (10/9) Discussion 7 has been uploaded.
- (10/5) Homework 5 solutions have been released. Homework 5 self-grades are due Monday, 10/9, 5 PM. Homework 6 has been released; it is due Thursday, 10/12.
- (10/4) Professor Walrand has provided companion notebooks for his textbook. Please check them out.
- (10/2) Discussion 6 has been uploaded.
- (9/29) Homework 4 solutions have been released. Homework 4 self-grades are due Monday, 10/2, 5 PM.
- (9/28) Homework 5 has been released; it is due Thursday, 10/5.
- (9/25) The deadline for Homework 4 has been extended to Friday, 9/28, 9 AM. Discussion 5 has been uploaded.
- (9/22) Homework 4 has been released; it is due Thursday, 9/28.
- (9/21) Discussion 4 has been uploaded. Lab 0 solutions have been released. Lab 1 solutions have been released. Lab 1 self-grades are due Monday, 9/25, 5 PM.
- (9/17) The Midterm 1 review worksheet has been uploaded.
- (9/15) Homework 2 solutions have been released. Homework 2 self-grades are due Monday, 9/18, 5 PM. Homework 3 has been released with solutions. You are not required to submit Homework 3. The Midterm 1 review session will be on Sunday, 9/17, 3-5 PM, 540AB Cory.
- (9/11) Discussion 3 has been uploaded.
- (9/7) Homework 1 solutions have been released. Homework 1 self-grades are due Monday, 9/11, 5 PM. Homework 2 has been released; it is due Thursday, 9/14. Labs 0 and 1 have been released. Lab 0 is optional: it is intended to introduce you to Python 3 and Jupyter Notebook, so we strongly recommend completing it. Lab 1 is due on Thursday, 9/21, 9 AM.
- (9/6) Discussion 2 has been uploaded.
- (8/31) Homework 1 has been released; it is due Thursday, 9/7. You can find the Gradescope entry code on Piazza. Since Monday (9/4) is a holiday, the discussion sections will be held on Wednesday 9/6, 2-4 PM, 521 Cory.
- (8/28) Discussion 1 has been uploaded.
- (8/25) Professor Walrand's OH have been updated to Tuesdays, 2:30-3:30 PM.
- (8/24) Homework parties will
**not**start until the third week.**Room Change: Starting on Tuesday, 8/29, the lecture will be held in 159 Mulford.**Also note that Professor Walrand's OH will be held in his office, 257 Cory. - Welcome to EE 126! Please see the syllabus and join Piazza.

## Course Information

### Staff

**Instructors**

- Abhay Parekh
- Jean Walrand

**Instructors' OH**: Professor Parekh will have OH on Thursdays, 2:45-3:45 PM. The location of the OH will change from week to week:

Dates | Location |
---|---|

8/29 - 9/5 | 212 Cory |

9/7 - 9/28 | 511 Soda |

10/3 - 10/24 | 212 Cory |

10/26 - 11/2 | 511 Soda |

11/7 - 12/7 | 373 Soda |

Professor Walrand will have OH on Tuesdays, 2:30-3:30 PM, in his office (257 Cory).

**TAs**

- Sinho Chewi. OH: Wednesday 3-4 PM, 521 Cory.
- Avishek Ghosh. OH: Wednesday 2-3 PM, 521 Cory.

**Homework Party**: The TAs will hold homework parties on Wednesdays, 5-7 PM, 531 Cory.

**Textbooks**

*Introduction to Probability*by Bertsekas and Tsitsiklis [2nd Edition] (B-T)*Probability in Electrical Engineering & Computer Science*by Walrand (W)- Python Notebooks for
*Probability in Electrical Engineering & Computer Science*by Walrand (WN)

For more detailed information, please look at the full syllabus.

The lectures will not be recorded this semester.

Date | Topics | Reading | Assignments |
---|---|---|---|

08/24 | Introduction/Logistics, Probability Spaces | B-T 1.1-1.2 | |

08/29 | Conditional Probability, Counting | B-T 1.3-1.6 | |

08/31 | Discrete Random Variables (Binomial, Poisson), Expectation, Variance | B-T 2.1-2.4 | HW 1 Released |

09/05 | Joint PMFs, Independence, Linearity of Expectation, Coupon Collector Problem, Entropy | B-T 2.5-2.8 | |

09/07 | Continuous Random Variables (Uniform, Exponential, Gaussian) | B-T 3.1-3.3 | HW 1 Due, HW 2 Released, Lab 1 Released |

09/12 | Joint PDFs, Continuous Conditional Probability | B-T 3.4-3.7 | |

09/14 | Conditional Expectation, Law of Total Variance, Transforms | B-T 4.1-4.6 | HW 2 Due, HW 3 Released |

09/19 | Markov's Inequality, Chebyshev's Inequality, Chernoff Bounds, Modes of Convergence, WLLN, SLLN, CLT | B-T 5.1-5.6 | |

09/21 | Midterm 1 |
HW 4 Released, Lab 1 Due | |

09/26 | CLT, Bernoulli Process | B-T 6.1 | |

09/28 | Poisson Process, Random Incidence | B-T 6.2-6.3 | HW 5 Released, HW 4 Due |

10/03 | Poisson Process, Random Incidence, PageRank | B-T 6.2-6.3 | |

10/05 | Discrete-Time Markov Chains | W 1, WN 1 | HW 6 Released, HW 5 Due |

10/10 | Discrete-Time Markov Chains | W 1, WN 1 | |

10/12 | Hidden Markov Models, Viterbi Algorithm | W 9.1-9.2, WN 9 | HW 7 Released, HW 6 Due |

10/17 | Multiplexing | W 3, WN 3 | |

10/19 | Multiplexing | W 3, WN 3 | HW 7 Due, Lab 2 Released |

10/24 | MLE, MAP, Hypothesis Testing, Neyman-Pearson Lemma | W 5, WN 5 | |

10/26 | Midterm 2 |
HW 8 Released | |

10/31 | MLE, Joint Gaussians | W 6.3-6.4, WN 6 | |

11/2 | Estimation, Kalman Filter | W 7, WN 7 | HW 8 Due, HW 9 Released |

11/7 | LLSE, Kalman Filter | W 7, WN 7 | |

11/9 | Updating the LLSE | W 8.1, WN 8 | HW 9 Due, HW 10 Released, Lab 3 Released |

11/14 | Kalman Filter, LQG | W 7-8, 12.1-12.2, Note on LQG | |

11/16 | MDPs | W 11 | HW 10 Due, HW 11 Released |

11/21 | Countable-State Markov Chains, CTMCs | W 13.3, 13.5 | |

11/28 | Entropy | ||

11/30 | Final Lecture | HW 11 Due |

## Discussions

Discussion worksheets will be posted here.

- Discussion 1 (Solutions)
- Discussion 2 (Solutions)
- Discussion 3 (Solutions)
- Midterm 1 Review (Solutions)
- Discussion 4 (Solutions)
- Discussion 5 (Solutions)
- Note: Modes of Convergence
- Discussion 6 (Solutions)
- Note: Wald's Identity
- Discussion 7 (Solutions)
- Discussion 8 (Solutions)
- Midterm 2 Review (Solutions)
- Discussion 9 (Solutions)
- Discussion 10 (Solutions)
- Discussion 11 (Solutions)
- Discussion 12 (Solutions)
- Discussion 13 (Solutions)
- Discussion 14 (Solutions)
- Final Review (Solutions)

## Homework

Homework will be posted here.

- Homework 1 (Solutions)
- Homework 2 (Solutions)
- Homework 3 (Solutions) (Optional)
- Homework 4 (Solutions)
- Homework 5 (Solutions)
- Homework 6 (Solutions)
- Homework 7 (Solutions)
- Homework 8 (Solutions)
- Homework 9 (Solutions)
- Homework 10 (Solutions)
- Homework 11 (Solutions)

## Labs

Labs will be posted here.