# Probability and Random Processes

Spring 2020

Kannan Ramchandran

TuTh 12:30-2 PM, Lewis 100

OH: Tuesday 2-3 Cory 212

## Announcements

- Lab 2 Sols are released. Self grades are due by Friday night (2/21) via this form.
- Homework 4 is released. It is due by Wednesday night (2/19) at 11:59PM.
- Homework 3 Sols are released. Self grades are due by Wednesday night (2/19) via this form.
- Midterm 1 logistics have been posted on Piazza. Check out the exams page for more information and resources.
- Discussions start this week (1/21-1/24), OH starts next week (1/27-1/31).
- Welcome to EECS 126! Please read the course info, join Piazza, and join Gradescope (code 9XJ64Z).

## Lecture Schedule

Lectures are not recorded. Subject to some changes.

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

1/21 | Introduction, Probability Spaces, Conditional Probability, Law of Total Probability | B-T 1 | HW 1 HW 1 Sol |

1/23 | Independence, Bayes Rule, Discrete Random Variables | B-T 1, 2 | Lab 0 Lab 0 Sol |

1/28 | Expectation, Uniform, Geometric, Binomial and Poisson Distributions | B-T 2 | HW 2 HW 2 Sol |

1/30 | (Co)variance, Correlation, Conditional / Iterated Expectation, Law of Total Variance | B-T 2 | Lab 1 Lab 1 Sol |

2/4 | Continuous Probability, Uniform, Exponential Distributions | B-T 3 | HW 3 HW 3 Sol |

2/6 | Gaussian Distribution, Derived Distributions, Continuous Bayes | B-T 3, 4.1-4.2 | Lab 2 Lab 2 Sol |

2/11 | Order Statistics, Convolution, Moment Generating Functions | B-T 4.3-4.6 | HW 4 |

2/13 | MGFs, Bounds/Concentration Inequalities (Markov, Chebyshev, Chernoff) | B-T 5.1 | TBA |

2/18 | Convergence, Weak and Strong Law of Large Numbers, Central Limit Theorem | Convergence | TBA |

2/20 | No Lecture (Midterm 2/21) | ||

2/25 | Information Theory | Information Theory | TBA |

2/27 | Binary Erasure Channel Capacity | Capacity of BEC | TBA |

3/3 | Discrete Time Markov Chains, Calculations, Stationary Distribution | Markov Chains | TBA |

3/5 | DTMCs: Infinite States, Classification, Big Theorem | TBA | |

3/10 | DTMCs: Reversibility, Hitting Time, First Step Equations | Reversibility | TBA |

3/12 | Poisson Processes: Counting Process, Memorylessness, Merging, Splitting | TBA | |

3/17 | PP: Erlang Distribution, Random Incidence | TBA | |

3/19 | Continuous Time Markov Chains: Rate Matrix and Stationary Distribution | TBA | |

3/31 | CTMCs: Big Theorem, First Step Equations and Jump Chain | TBA | |

4/2 | No Lecture (Midterm 4/3) | ||

4/7 | Erdos-Renyi Random Graphs | Random Graphs | TBA |

4/9 | Maximum Likelihood Estimation, Maximum a Posteriori Estimation | TBA | |

4/14 | Statistical Hypothesis Testing, Neyman-Pearson Lemma | Hypothesis Testing | TBA |

4/16 | Minimum Mean Square Error Estimation, Vector Space of Random Variables | Hilbert Space | TBA |

4/21 | Linear Least Square Estimate | TBA | |

4/23 | Jointly Guassian Random Variables | TBA | |

4/28 | Orthogonal Updates and Kalman Filter | Geometric Derivation of Scalar Kalman Filter | TBA |

4/30 | Fisher Information and Cramer Rao Bound | TBA |