# EECS 126: Probability & Random Processes

## Announcements

- (5/5) Solutions to optional labs have been uploaded.
- (5/3) Homework 13 Solutions have been uploaded.
- (5/1) Homework 12 Solutions have been uploaded; self-grades are due Friday, 5/4, 5 PM.
- (4/30) Homework 13 has been uploaded; you are not required to complete it. Solutions will be released in a few days.
- (4/27) The optional labs (choose one) have been released and are due Friday 5/4 at 5 PM for an extra lab drop. The optional course survey (please fill it out!) can be found here and filled in for an extra homework drop. Lab 7 Solutions have been uploaded; self-grades are due Monday, 4/30, 5 PM. Discussion 14 has been uploaded.
- (4/25) The deadline for Homework 12 has been extended to Monday, 4/30, 5 PM.
- (4/20) Homework 12 has been uploaded; it is due Friday, 4/27, 5 PM. Lab 7 has been uploaded; it is due Friday, 4/27, 5 PM. Homework 11 Solutions have been uploaded; self-grades are due Monday, 4/23, 5 PM. Discussion 13 has been uploaded.
- (4/17) Project deadline extended to Wednesday 4/18 11:59 PM.
- (4/14) Discussion 12 has been uploaded.
- (4/13) The due date of Homework 11 has been pushed back to Friday, 4/20, 5 PM.
- (4/12) Homework 11 has been uploaded; it is due Wednesday, 4/18, 11:59 PM. Homework 10 Solutions have been uploaded; self-grades are due Monday, 4/16, 5 PM.
- (4/10) Professor Ramchandran's office hours will be moved back to 4:30-5:30 today.
- (4/6) Lab 6 Solutions have been uploaded; self-grades are due Monday, 4/9, 5 PM. Discussion 11 has been uploaded.
- (4/2) Lab 6 has been uploaded; it is due Friday, April 6, 9:59 AM. Homework 10 has been uploaded; it is due Wednesday, 4/11, 11:59 PM.
- (3/23) Discussion 10 has been uploaded.
- (3/20) Homework 9 Solutions have been uploaded; self-grades are due Monday, 4/2.
- (3/16) Homework 8 Solutions and Lab 5 Solutions have been uploaded; self-grades are due Monday, 3/19. Discussion 9 has been uploaded.
- (3/15) Homework 9 has been uploaded; it is due Monday, 3/19. The Project has been uploaded; the proposal is due Wednesday, April 4, 9:59 AM, and the final project is due Wednesday, April 18, 9:59 AM. The website has been updated with information about Midterm 2.
- (3/10) Homework 7 Solutions have been uploaded; self-grades are due Monday, 3/12.
- (3/9) Homework 8 has been uploaded; it is due Wednesday, 3/14. Discussion 8 has been uploaded.
- (3/6) Lab 5 has been uploaded; it is due Friday 3/16.
- (3/1) Homework 7 has been uploaded; it is due Wednesday, 3/7. Homework 6 Solutions and Lab 4 Solutions have been uploaded; self-grades are due Monday, 3/5. Discussion 7 has been uploaded.
- (2/23) Homework 6 has been uploaded; it is due Wednesday, 2/28. Homework 5 Solutions have been uploaded; self-grades are due Monday, 2/26. Discussion 6 has been uploaded.
- (2/18) Lab 4 has been uploaded. Due to the late release time, it will be due Friday, 3/2. Discussion 5 has been uploaded.
- (2/15) Homework 5 has been uploaded; it is due Wednesday, 2/21.
- (2/13) There is no Lab Party this week. Homework 4 Solutions have been uploaded; self-grades are due Monday, 2/19.
- (2/9) Homework 3 Solutions and Lab 3 Solutions have been uploaded; self-grades are due Monday, 2/12. Discussion 4 has been uploaded.
- (2/8) The website has been updated with information about Midterm 1.
- (2/7) Homework 4 has been uploaded; it is due Monday, 2/12.
- (2/2) Homework 3 has been uploaded; it is due Wednesday, 2/7. Lab 3 has been uploaded; it is due Friday, 2/9. Homework 2 Solutions and Lab 2 Solutions have been uploaded; self-grades are due Monday, 2/5. Discussion 3 has been uploaded.
- (1/31) DIS 206 has been moved to Friday, 4-5 PM, 521 Cory.
- (1/25) Homework 2 has been uploaded; it is due Wednesday, 1/31. Lab 2 has been uploaded; it is due Friday, 2/2. Homework 1 Solutions and Lab 1 Solutions have been uploaded; self-grades are due Monday, 1/29. Discussion 2 has been uploaded.
- (1/20) The Diagnostic Quiz and Discussion 1 have been uploaded.
- (1/19) Lab 1 has been uploaded; it is due Friday, 1/26.
- (1/16) Homework 1 has been uploaded; it is due Wednesday, 1/24.
- Welcome to EECS 126! Please read the syllabus and join Piazza. Discussion sections
**will**be held on the first week of class. Homework party, lab party, and OH will begin on Monday, 1/22.

## Course Information

**Lectures**: Tuesday/Thursday, 2-3:30 PM, 100 Lewis

### Staff

**Instructors**

- Kannan Ramchandran. OH: Tuesday, 4-5 PM, 269 Cory.

**TAs**

- Tavor Baharav
- DIS 201: Wednesday, 9-10 AM, 209 Dwinelle.
- OH: Wednesday, 2-4 PM, 212 Cory.
- Kaylee Burns
- DIS 205: Friday, 11-12 PM, 521 Cory.
- OH: Tuesday, 11-12 PM, 611 Soda.
- Gary Cheng
- DIS 203: Wednesday, 11-12 PM, 3113 Etcheverry.
- OH: Tuesday, 12-1 PM, 611 Soda.
- Sinho Chewi
- DIS 204: Wednesday, 8-9 AM, 521 Cory.
- OH: Tuesday, 6-8 PM, 504 Cory.
- Hemang Jangle
- DIS 206: Friday, 4-5 PM, 521 Cory.
- OH: Monday, 1-2 PM, 341B Soda.
- Alvin Kao
- DIS 207: Friday, 10-11 AM, 293 Cory.
- OH: Monday, 4-5 PM, 611 Soda.
- Vrettos Moulos
- DIS 202: Wednesday, 10-11 AM, 140 Barrows.
- OH: Monday, 2-4 PM, 283E Soda.
- Ray Ramamurti
- DIS 208: Friday, 12-1 PM, 293 Cory.
- OH: Wednesday, 12-1 PM, 341A Soda.

**Readers**

- William Gan
- Chen Meng
- Kanaad Parvate

**Homework Party**: Monday, 6:30-9 PM, 521 Cory.

**Lab Party**: Thursday, 6-8 PM, 212 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 |
---|---|---|---|

01/16 | Introduction/Logistics, Probability Spaces/Axioms, Conditional Probability, Multiplication Rule, Law of Total Probability, Bayes Rule, Independence | B-T 1 | HW 1 (due 1/24) |

01/18 | Discrete Random Variables, Probability Mass Functions (PMFs), Joint Distributions, Expectation, Binomial Distribution, Poisson Distribution | B-T 2 | Lab 1 (due 1/26) |

01/23 | St. Petersburg Paradox, Conditioning of Random Variables, Independence of Random Variables, Variance, Covariance, Cumulative Distribution Function (CDF), Tail Sum Formula, Geometric Distribution (Memoryless Property), Coupon Collection | B-T 2 | |

01/25 | Correlation, Poisson Properties, Entropy | B-T 2 | HW 1 Self-Grades (due 1/29), Lab 1 Self-Grades (due 1/29), HW 2 (due 1/31), Lab 2 (due 2/2) |

01/30 | Continuous Sample Spaces, Continuous Random Variables, Probability Density Function (PDF), Uniform Distribution, Exponential Distribution (Memoryless Property) | B-T 3 | |

02/01 | Order Statistics, Gaussian Distribution, Derived Distributions, Convolution | B-T 3, B-T 4.1-4.2 | HW 2 Self-Grades (due 2/5), Lab 2 Self-Grades (due 2/5), HW 3 (due 2/7), Lab 3 (due 2/9) |

02/06 | Transforms, Moments, Moment Generating Functions (MGFs) | B-T 4.3-4.6 | |

02/08 | Markov's Inequality, Chebyshev's Inequality, Chernoff Bound | B-T 5.1, W 13.7 | HW 3 Self-Grades (due 2/12), Lab 3 Self-Grades (due 2/12), HW 4 (due 2/12) |

02/13 | Weak Law of Large Numbers (WLLN), Convergence in Probability, Strong Law of Large Numbers (SLLN), Almost Sure Convergence, Central Limit Theorem (CLT) | B-T 5.2-5.6, W 2.1-2.3, Modes of Convergence | |

02/15 | No Lecture | HW 4 Self-Grades (due 2/19), HW 5 (due 2/21), Lab 4 (due 3/2) | |

02/20 | Digital Communication, Capacity of the Binary Erasure Channel (BEC) | ||

02/22 | Achievability of the BEC Capacity, Discrete-Time Markov Chains (DTMCs) | Capacity of the BEC, W 1, 2.4, 13.3, B-T 7.1-7.4 | HW 5 Self-Grades (due 2/26), HW 6 (due 2/28) |

02/27 | DTMCs: Irreducibility, Aperiodicity, Balance Equations, Big Theorem | W 1, 2.4, 2.6, 13.3, B-T 7.1-7.4 | |

03/01 | DTMCs: PageRank, Classification, Infinite State Space, First-Step Equations (FSE) | W 1, 2.4, 2.6, 13.3, B-T 7.1-7.4, Supplemental Notes | HW 6 Self-Grades (due 3/5), Lab 4 Self-Grades (due 3/5), HW 7 (due 3/9), Lab 5 (due 3/16) |

03/06 | DTMCs: Absorption, Reversibility; Poisson Process: Construction | Reversibility, B-T 6.1-6.3, W 13.4 | |

03/08 | Poisson Process: Memorylessness, Merging, Splitting | B-T 6.1-6.3, W 13.4 | HW 7 Self-Grades (due 3/12), HW 8 (due 3/14) |

03/13 | Poisson Process: Erlang Distribution, Random Incidence; Continuous-Time Markov Chains (CTMCs): Introduction, Markov Property, Rate Matrix | B-T 7.5, W 13.5 | |

03/15 | CTMCs: Balance Equations, Big Theorem, FSE | B-T 7.5, W 13.5 | HW 8 Self-Grades (due 3/19), Lab 5 Self-Grades (due 3/19), HW 9 (due 3/19), Project (proposal due 4/4) |

03/20 | Random Graphs | Random Graphs | HW 9 Self-Grades (due 4/2) |

03/22 | Maximum Likelihood Estimation (MLE), Maximum A Posteriori (MAP) Estimation | W 5.1, B-T 8.1-8.2, 9.1 | |

03/27 | Spring Break | ||

03/29 | Spring Break | ||

04/03 | Inference (Digital Communication) | W 5.1-5.4, B-T 8.1-8.2, 9.1 | Lab 6 (due 4/6), HW 10 (due 4/11) |

04/05 | Hypothesis Testing | W 5.5-5.6, 6.5, B-T 9.3-9.4 | Lab 6 Self-Grades (due 4/9), Project (due 4/18) |

04/10 | Linear Least Squares Estimation (LLSE), Vector Space of Random Variables | W 7.1-7.5, B-T 8.3-8.5, Hilbert Space of Random Variables | |

04/12 | Signal-to-Noise Ratio (SNR), Minimum Mean Square Error (MMSE) Estimation | W 6.3-6.4, 8.1 | HW 10 Self-Grades (due 4/16), HW 11 (due 4/20) |

04/17 | Joint Gaussians, Gram-Schmidt Process | W 7.6-7.7, 8.1-8.2 | |

04/19 | Kalman Filter | W 9.1-9.2, 9.4, A Geometric Derivation of the Scalar Kalman Filter, Lecture Notes | HW 11 Self-Grades (due 4/23), Lab 7 (due 4/27), HW 12 (due 4/30) |

04/24 | Hidden Markov Models (HMMs), Viterbi Algorithm | W 9.1-9.4, Lecture Notes | |

04/26 | Clustering, Expectation Maximization (EM) Algorithm | W 9.1-9.4, Lecture Notes | HW 12 Self-Grades (due 5/4), Lab 7 Self-Grades (due 4/30) |

## Discussions

Discussion worksheets will be posted here.

- Diagnostic Quiz (Solutions)
- Discussion 1 (Solutions)
- Discussion 2 (Solutions)
- Discussion 3 (Solutions)
- Discussion 4 (Solutions)
- Discussion 5 (Solutions)
- Discussion 6 (Solutions)
- Discussion 7 (Solutions)
- Discussion 8 (Solutions)
- Discussion 9 (Solutions)
- Discussion 10 (Solutions)
- Discussion 11 (Solutions)
- Discussion 12 (Solutions)
- Discussion 13 (Solutions)
- Discussion 14 (Solutions)

## Homework

Homework will be posted here.

- Homework 1 (Solutions)
- Homework 2 (Solutions)
- Homework 3 (Solutions)
- Homework 4 (Solutions)
- Homework 5 (Solutions)
- Homework 6 (Solutions)
- Homework 7 (Solutions)
- Homework 8 (Solutions)
- Homework 9 (Solutions)
- Homework 10 (Solutions)
- Homework 11 (Solutions)
- Homework 12 (Solutions)
- Homework 13 (Solutions)

## Labs

Labs will be posted here.

- Lab 1 (Solutions)
- Lab 2 (Solutions)
- Lab 3 (Solutions)
- Lab 4 (Solutions)
- Lab 5 (Solutions)
- Project (PDF)
- Catan
- Markov Chains: PageRank / MCMC
- Digital Communications (no additional material required)

- Lab 6 (Solutions)
- Lab 7 (Solutions)
- Optional labs

## Exams

### Midterm 1

**Location**: 2050 VLSB

**Time**: Wednesday, February 14, 7-9 PM

**Logistics**: No electronics are allowed. No cheat sheets are allowed; we will provide a cheat sheet of our own. For DSP accommodations, please email the course staff.

**Resources**: Past Exams (*Disclaimer*: The content covered in the course has changed over the years, so older exams may not necessarily be representative of the material that will be covered on the midterm.)

**Review Session**: Wozniak Lounge, Saturday, February 10, 4-6 PM.

### Midterm 2

**Location**: 2050 VLSB

**Time**: Wednesday, March 21, 7-9 PM

**Logistics**: No electronics are allowed. No cheat sheets are allowed; we will provide a cheat sheet of our own. For DSP accommodations, please email the course staff.

**Resources**: Past Exams (*Disclaimer*: The content covered in the course has changed over the years, so older exams may not necessarily be representative of the material that will be covered on the midterm.)

**Review Session**: 306 Soda, Friday, March 16, 6:30-8:30 PM.

### Final

**Location**: TBA

**Time**: Monday, May 7, 11:30-2:30 PM

**Logistics**: No electronics are allowed. No cheat sheets are allowed; we will provide a cheat sheet of our own. For DSP accommodations, please email the course staff.

**Resources**: Past Exams (*Disclaimer*: The content covered in the course has changed over the years, so older exams may not necessarily be representative of the material that will be covered on the midterm.)

**Review Session**: 100 Lewis, Tuesday, May 1, 2-3:30 PM.