# Probability and Random Processes

Fall 2019

Shyam Parekh

TuTh 11-12:30 PM, Evans 10

## Announcements

- Lab 2 has been uploaded and is due Friday 9/20.
- Homework 3 has been uploaded and is due FRIDAY 9/20.
- Lab 1 Solutions have been uploaded and self grades are due Monday 9/16.
- Homework 2 Solutions have been uploaded and self grades are due Monday 9/16.
- Welcome to EECS 126! Please read the course info, join Piazza, and join Gradescope (code 95RY4R).

## Lecture Schedule

Lectures are not recorded. Subject to some changes.

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

08/29 | Introduction, Probability Spaces, Conditional Probability, Law of Total Probability | B-T 1 | HW 1 HW 1 Sol |

09/03 | Independence, Bayes Rule, Discrete Random Variables | B-T 1, 2 | Lab 0 Lab 0 Sol |

09/05 | Expectation, Uniform, Geometric, Binomial and Poisson Distributions | B-T 2 | HW 2 HW 2 Sol |

09/10 | (Co)variance, Correlation, Conditional / Iterated Expectation, Entropy | B-T 2 | Lab 1 Lab 1 Sol |

09/12 | Entropy, Continuous Probability, Uniform, Exponential Distributions | B-T 3 | HW 3 Lab 2 |

09/17 | Gaussian Distribution, Derived Distributions, Continuous Bayes | B-T 3, 4.1-4.2 | TBA |

09/19 | Order Statistics, Convolution, Moment Generating Functions | B-T 4.3-4.6 | TBA |

09/24 | MGFs, Bounds/Concentration Inequalities (Markov, Chebyshev, Chernoff) | B-T 5.1 & W 13.7 | TBA |

09/26 | No Lecture (Midterm 1) | TBA | |

10/01 | Convergence, Weak and Strong Law of Large Numbers, Central Limit Theorem | B-T 5.2-5.6, W 2.1-2.3 | TBA |

10/03 | CLT, Information Theory, Capacity of the Binary Erasure Channel (BEC) | Capacity of a BEC | TBA |

10/08 | Achievability of BEC Capacity, Markov Chains Introduction | W 1, 13.3, B-T 7.1-7.4 | TBA |

10/10 | Discrete Time Markov Chains: Invariant Distribution and Balance Equations | W 1, 2.4, 2.6, 13.3, B-T 7.1-7.4 | TBA |

10/15 | DTMCs: Hitting Time, First Step Eqs (FSEs), Infinite States, Classification, Big Theorem | W 1, 2.4, 2.6, 13.3, B-T 7.1-7.4, Markov Chains | TBA |

10/17 | DTMCs: Classification, Reversibility, Poisson Processes: Construction | B-T 6.1-6.3, W 13.4, Reversibility | TBA |

10/22 | Poisson Processes: Counting Process, Memorylessness, Merging, Splitting | B-T 6.1-6.3, W 13.4 | TBA |

10/24 | PP: Erlang Distribution, Random Incidence, Continuous Time Markov Chains Intro, Rate Matrix | B-T 7.5, W 13.5 | TBA |

10/29 | CTMCs: Balance Equations, Big Theorem, FSEs | B-T 7.5, W 13.5 | TBA |

10/31 | CTMCs: Simulated DTMC, Erdos-Renyi Random Graphs | Random Graphs | TBA |

11/05 | No Lecture (Midterm 2) | TBA | |

11/07 | Maximum Likelihood Estimation, Maximum A Posteriori Estimation | W 5.1, B-T 8.1-8.2, 9.1 | TBA |

11/12 | MLE/MAP, Neyman Pearson Hypothesis Testing | W 5.1, B-T 8.1-8.2, 9.1/ W 5.5-5.6, 6.5, B-T 9.3-9.4, Hypothesis Testing | TBA |

11/14 | Vector Space of Random Variables and Least Squares Estimation | W 5.5-5.6, 6.5, B-T 9.3-9.4/ W 7.1-7.5, B-T 8.3-8.5 Hilbert Space of Random Variables | TBA |

11/19 | Linear Least Squares Estimation, Minimum Mean Square Error (MMSE) Estimation | W 7.1-7.5, B-T 8.3-8.5 | TBA |

11/21 | MMSE, Gram Schmidt Process | W 7.1-7.5, W 8.1 | TBA |

11/26 | Jointly Gaussian Random Variables, Kalman Filter | W 6.3-6.4, 7.6, 8.1-8.3 Geometric Derivation of Scalar Kalman Filter | TBA |

11/28 | No Lecture (Thanksgiving) | TBA | |

12/03 | Kalman Filter | W 7.6, 8.1-8.3 | TBA |

12/05 | Hidden Markov Models | W 9.2,9.4 HMMs and the Viterbi Algorithm | TBA |