# EECS 126: Probability & Random Processes

## Announcements

- (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 2/23) | |

02/20 | Capacity of the Binary Erasure Channel (BEC) | Notes | |

02/22 | Discrete-Time Markov Chains (DTMCs) | W 1, B-T 7.1-7.4 | HW 5 Self-Grades (due 2/26), Lab 4 Self-Grades (due 2/26), HW 6 (due 2/28) |

## 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)

## Homework

Homework will be posted here.

- Homework 1 (Solutions)
- Homework 2 (Solutions)
- Homework 3 (Solutions)
- Homework 4 (Solutions)
- Homework 5

## Labs

Labs will be posted here.

## 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