# EECS 126: Probability & Random Processes - Fall 2018

## Announcements

- (12/10) Solutions to optional labs posted.
- (12/6) Homework 14 and Lab 7 solutions have been released. Self grades are due
**Friday, 12/7 at 11.59pm** - (11/28) Homework 13 solutions have been posted. Self grades are due
**Monday, 12/3 at 5pm** - (11/28) Homework 14 and Lab 7 have been released. They are both due
**Tuesday, 12/4 at 11.59pm** - (11/15) Homework 12 Solutions have been uploaded. Self grades are due
**Monday, 11/19 at 5pm**. - (11/15) Homework 13 has been released.It is due
**Tuesday, 11/27 at 11.59p.m.** - (11/8) Homework 12 has been released. It is due
**Wednesday, 11/14 at 11.59p.m.** - (11/1) Homework 10 Solutions have been uploaded. Self grades are due
**Monday, 11/5 at 5pm**. - (11/1) Homework 11 has been uploaded. It is not graded but the content is in scope for the midterm.
- (10/25) Homework 10 has been uploaded. It is due
**Wednesday, 10/31 at 11.59pm**. Homework 9 solutions have been uploaded. Self grades are due**Monday, 10/29 at 5pm.** - (10/25) Discussion 10 has been uploaded. Discussion 9 solutions uploaded.
- (10/20) Lab 6 solutions have been uploaded. Self grades for Lab 6 and HW8 are due
**Monday, 10/22 at 5pm.** - (10/18) Homework 9 has been uploaded. It is due
**Wednesday, 10/24 at 11.59 pm**. HW8 solutions have been released. - (10/18) Discussion 9 and Discussion 8 solutions have been uploaded.
- (10/16) Project descriptions released along with Catan starter code and Page Rank introduction notebook.
- (10/12) Lab 5 solutions have been released. Self grades for Lab 5 and Homework 7 are due at
**5pm on Monday, 10/15** - (10/12) Lab 6 has been released. It is due
**Friday, 10/19 at 10am.** - (10/11) Homework 8 has been uploaded. It is due
**Wednesday, 10/17 at 11.59pm.** - (10/11)Solutions to Homeowork 7 and Discussion 7 have been uploaded.
- (10/5) Lab 5 has been released. It is due
**Friday, 10/12 at 10.am** - (10/5) Lab 4 solutions have been released. Self grades for Lab 4 and HW 6 are due
**Monday, 10/8 at 5pm** - (10/4) Homework 6 solutions have been uploaded. Discussion 6 has been uploaded.
- (10/4) Homework 7 has been released. It is due
**Wednesday, 10/10 at 11.59 pm** - (9/28) Homework 5 solutions have been uploaded. Self grades are due
**Monday, 10/1 at 5pm** - (9/28) Lab 4 has been uploaded. It is due
**Friday, 10/5 at 10am.** - (9/28) Discussion 5 has been uploaded.
- (9/26) Homework 6 has been released. It is due next Wednesday, 10/3 at 11.59pm.
- (9/25) Homework 5 deadline has been extended 24 hrs. Its now due at
**11.59pm, Thursday, 9/27** - (9/20) Homework 5 has been released. It is due Wednesday, 9/26, 11.59pm. There is no lab this week. Please fill out the post midterm survey here
- (9/18)Discussion 4 solutions uploaded.
- (9/16) HW4 solutions released.
- (9/14) Lab 3 solutions released. Self grades due Monday, 9/17.
- (9/13) Homework 3 solutions have been uploaded. Homework 4 has been uploaded. It is optional.
- (9/7) Lab 3 has been uploaded. It is due on Friday, 9/14 at 10am.
- (9/7) Lab 2 solutions and self grades have been uploaded. Self grades are due Monday, 9/10 at 5pm.
- (9/6) Discussion 3 has been uploaded.
- (9/6) Homework 3 has been uploaded; it is due Wednesday, 9/12. Homework 2 solutions have been uploaded.
- (8/31) Lab 2 has been uploaded; it is due Friday, 9/7.
- (8/31) Lab 1 self grades uploaded. Self grades for both HW1 and Lab1 are due on
**Saturday (9/1)**just for this week - (8/30) Discussion 2 has been uploaded.
- (8/30) Homework 2 has been uploaded. It is due Wednesday, 9/5. Homework 1 Solutions have been uploaded.
- (8/27) HW Party location has been changed for tonight and on 9/10. Please see @37 on Piazza.
- (8/24) Lab 1 has been uploaded; it is due Friday, 8/31.
- (8/23) Discussion 1 has been uploaded.
- (8/23) Homework 1 has been uploaded; it is due Wednesday, 8/29.
- Welcome to EECS 126! Please read the syllabus and join Piazza. Discussion sections will begin on Friday (8/24). Homework party, lab party, and OH will begin on Monday, 8/27.

## Course Information

**Lectures**: Tuesday/Thursday, 11-12:30 PM, 105 Stanley

### Staff

**Instructors**

- Kannan Ramchandran. OH: Tuesday, 1-2 PM, 400 Cory.
- Abhay Parekh. OH: Thursday, 1-2 PM, 504 Cory.

**NOTE:**

- Professor Ramchandran's OH on Tuesday, 9/18 will be in Cory 269.
- Professor Parekh's OH on the following Thursdays will be in 400 Cory - 9/6, 9/20, 9/27, 10/4, 10/11

**TAs**

- Kurtland Chua
- DIS 203: Monday, 4-5PM, Dwinelle 182
- OH: Tuesday, 3-4PM, Soda 651
- Payam Delgosha
- DIS 201: Monday 2-3PM, Haviland 12
- OH: Monday, 12-2PM, Cory 258
- William Gan
- DIS 205: Wednesday, 3-4PM, Dwinelle 88
- OH: Wednesday, 2-3PM, Soda 341A
- Avishek Ghosh
- DIS : N/A
- OH: Monday, 1-3PM, Soda 283H
- Justin Hong
- DIS : N/A
- OH: Tuesday, 2-3PM, Soda 341B
- Nikunj Jain
- DIS 210: Friday, 1-2PM, Cory 299
- OH: Monday, 5-6PM, Soda 651 & Wednesday, 4-5PM, Soda 283E
- Katie Kang
- DIS 204: Wednesday, 2-3PM, Wheeler 204
- OH: Monday, 3-4PM, Soda 341B
- Kanaad Parvate
- DIS 202: Monday, 3-4PM, Hearst Mining 310
- OH: Wednesday, 1-2PM, Soda 341A
- Ray Ramamurti
- DIS 209: Wednesday, 1-2PM, Cory 299
- OH: Wednesday, 4-6PM, Soda 411
- Amay Saxena
- DIS 206: Wednesday, 4-5PM, Dwinelle 182
- OH: Wednesday, 3-4PM, Soda 341A

**Readers**

- Raghav Anand
- Adarsh Karnati
- Eric Liu

**Homework Party**: Monday, 6-8 PM, 540AB Cory (DOP Center).

**Lab Party**: Thursday, 6-8 PM, 400 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 |
---|---|---|---|

08/23 | Introduction/Logistics, Probability Spaces/Axioms, Conditional Probability, Multiplication Rule, Law of Total Probability, Bayes Rule | B-T 1 | HW 1 (due 8/29), Lab 1 (due 8/31) |

08/28 | Bayes Rule, Independence, Conditional Independence, Discrete Random Variables | B-T 1, B-T 2 | |

08/30 | Discrete R.V.s, Expectation, Linearity, St.Petersburg Paradox, Variance | B-T 2 | HW 1 Self-Grades (due 9/1), Lab 1 Self-Grades (due 9/1), HW 2 (due 9/5), Lab 2 (due 9/7) |

09/04 | Continuous Random Variables, Probability Density Function (PDF), Uniform Distribution, Exponential Distribution (Memoryless Property), Derived Distributions, Convolution | B-T 3, B-T 4.1 | |

09/06 | Normal Distribution, Joint PDFs, Marginal PDFs, Conditional PDFs, Covariance | B-T 3, B-T 4.1, B-T 4.2 | HW 2 Self-Grades (due 9/10), HW 3 (due 9/12), Lab 2 Self Grades (due 9/10), Lab 3 (due 9/14) |

09/11 | Covariance, Correlation, Conditional Expectation, Iterated Expectation Diagnostic Quiz(Solutions) | B-T 4.2, B-T4.3 | |

09/13 | Moment Generating Functions, Markov's Inequality, Chebyshev's Inequality, Chernoff Bounds | B-T 4.4, B-T 4.5, B-T 5.1 | HW3 Self Grades(due 9/17), HW4 (optional) |

09/18 | Chernoff Bounds, Convergence, Weak and Strong Law of Large Numbers, Central Limit Theorem | B-T 5, W 2.1 - 2.3 | Homework 5(due 9/27) |

09/20 | No Lecture | ||

09/25 | Convergence, Discrete Time Markov Chains (Markov Property, Transition Matrix) | B-T 5, W 2.1-2.3 Modes of Convergence, B-T 7, W 1 | |

09/27 | Discrete Time Markov Chains (Recurrence,Transience, Stationary Distribution and Balance Equations, FSEs and Hitting Time | B-T 7, W 1, 2.4, 2.6, 13.3 | HW 5 Self Grades(due 10/1), Homework 6(due 10/3), Lab 4(due 10/5), |

10/2 | Discrete Time Markov Chains (Long Term Average, Positive Recurrence, Null Recurrence, Transience) | B-T 7, W 1, 2.4, 2.6, 13.3, Markov Chains Note | |

10/4 | Information Theory (Entropy, Source Coding, Typical Sets, Asymptotic Equipartition Property, Huffman Codes) | Information Theory | Homework 7 (due 10/10), HW 6 Self Grades(due 10/8), Lab 4 Self Grades (due 10/8), Lab 5 (due 10/12) |

10/9 | Information Theory (BSC, BEC, Channel Capacity) | Capacity of the BEC | |

10/11 | Erdos-Renyi Random Graphs | Random Graphs | Homework 8 (due 10/17), HW7 Self Grades (due 10/15), Lab 6 (due 10/19), Lab 5 Self Grades (due 10/15) |

10/16 | Random Graphs, Poisson Process Setup | B-T 6.1 - 6.3, W 13.4 | |

10/18 | Poisson Processes, Merging, Splitting, Erlang Distribution | B-T 6.1 - 6.3, W 13.4 | Homework 9 (due 10/24), HW8 Self Grades (due 10/22), , Lab 6 Self Grades (due 10/22) |

10/23 | Erlang Distribution, Random Incidence Paradox, Continuous Time Markov Chains | B-T 6.1 - 6.3, W 13.4, B-T 7.5, W 13.5 | |

10/25 | Continuous Time Markov Chains, Stationary Distribution, Hitting Time | B-T 7.5, W 13.5 | Homework 10, HW9 Self Grades |

10/30 | CTMCs-Embedded Markov Chain, MLE/MAP, Inference, Digital Communication | B-T 7.5, W 13.5, B-T 8.1-8.2, 9.1, W 5.1 | |

11/1 | MAP Inference in Digital Communication | W 5.1 - 5.4 | Homework 11, HW 10 Self Grades(due 11/5) |

11/6 | Neyman-Pearson Hypothesis Testing | W 5.5-5.6, B-T 9.3 | |

11/8 | Neyman Pearson Proof, Linear Least Squares Estimator, Vector Space of Random Variables | W-6.5, W 7.1-7.3, B-T 8.4, Hilbert Space of Random Variables | Homework 12(due 11/14) |

11/13 | LLSE, MMSE, Multivariate Gaussians | W 7.1-7.5, W 6.3-6.4, B-T 8.4-8.5 | |

11/15 | MMSE, Jointly Gaussian R.V.s, Kalman Filter | W 6.3-6.4,7.1-7.7, B-T 8.4-8.5, W-8.1 | Homework 13 (due 11/21), HW12 Self Grades(due 11/19) |

11/20 | Lecture Cancelled | ||

11/22 | Thanksgiving | ||

11/27 | Kalman Filter | W 7.6, 8.1-8.3, A Geometric Derivation of the Scalar Kalman Filter , Lecture Notes | Homework 14 (due 12/4), HW13 Self Grades (due 12/3), Lab 7 (due 12/4) |

11/29 | Hidden Markov Models, Viterbi Algorithm | W 9.1-9.2, Lecture Notes | |

12/4 | Expectation Maximization | W 9.3, Lecture Notes | HW14 Self Grades (due 12/7), Lab 7 Self Grades (due 12/7) |

## Discussions

Discussion worksheets will be posted here.

- 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) (Self Grades)
- Homework 2 (Solutions) (Self Grades)
- Homework 3 (Solutions) (Self Grades)
- Homework 4 (Solutions)
- Homework 5 (Survey) (Solutions) (Self Grades)
- Homework 6 (Solutions) (Self Grades)
- Homework 7 (Solutions) (Self Grades)
- Homework 8 (Solutions) (Self Grades)
- Homework 9 (Solutions) (Self Grades)
- Homework 10 (Solutions) (Self Grades)
- Homework 11 (Solutions)
- Homework 12 (Solutions) (Self Grades)
- Homework 13 (Solutions) (Self Grades)
- Homework 14 (Solutions) (Self Grades)

## Labs

Labs will be posted here.

- Lab 1 (Solutions)
- Lab 2 (Solutions)
- Lab 3 (Solutions)
- Lab 4 (Solutions)
- Lab 5 (Solutions)
- Lab 6 (Solutions)
- Project(PDF)
- Catan Code
- Page Rank Introduction
- No additional material required for Financial Modelling or Digital Communication

- Lab 7 (Solutions)
- Optional Labs:

## Exams

### Midterm 1

**Location**: VLSB 2050

**Time**: Wednesday, September 19, 8-10 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**: Hearst Field Annex A1, Sunday, September 16, 2-4 PM.

### Midterm 2

**Location**: Dwinelle 155

**Time**: Wednesday, November 7, 8-10 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**: GPB 100, Sunday, November 4, 2-4 PM.

### Final

**Location**: Stanley 105, Hearst Gym 234, Barrows 56 (please see piazza for details)

**Time**: Wednesday, December 12, 8-11 AM

**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**: Stanley 105, Thursday, December 6, 11AM -12.30 PM (during lecture)