# Probability and Random Processes

Fall 2022

Kannan Ramchandran

Lecture: TuTh 12:30-2 PM (Birge 50)

Office Hours: Tu 2-3 PM (Cory 212)

## Announcements

- Welcome to EECS 126! Please read the course info and join Ed. If you cannot access the Ed link, please email the Head TAs.
- Time conflicts will be allowed for this course but there will not be an alternate final exam time. Please make sure that your exam times don’t conflict with other classes you’re taking!

## Lecture Schedule

Schedule is subject to some changes.

Date | Topics | Readings |
---|---|---|

08/25 | Introduction, Probability Spaces, Conditional Probability, Law of Total Probability | B-T 1 |

08/30 | Independence, Bayes Rule, Discrete Random Variables | B-T 1, 2 Random Variables |

09/01 | Expectation, Uniform, Geometric, Binomial and Poisson Distributions | B-T 2 |

09/06 | (Co)variance, Correlation, Conditional / Iterated Expectation, Law of Total Variance | B-T 2 |

09/08 | Continuous Probability, Uniform, Exponential Distributions | B-T 3 |

09/13 | Gaussian Distribution, Derived Distributions, Continuous Bayes | B-T 3, 4.1-4.2 |

09/15 | Order Statistics, Convolution, Moment Generating Functions | B-T 4.3-4.6 |

09/20 | MGFs, Bounds/Concentration Inequalities (Markov, Chebyshev, Chernoff) | B-T 5.1 |

09/22 | Convergence, Weak and Strong Law of Large Numbers, Central Limit Theorem | B-T 5.2-5.6, W 2.1-2.3 Convergence |

09/27 | Information Theory | Information Theory |

09/29 | No Lecture (Midterm) | |

10/04 | Binary Erasure Channel Capacity | W 1, 13.3, B-T 7.1-7.4 Capacity |

10/06 | Information Theory Wrapup | |

10/11 | Discrete Time Markov Chains, Stationary Distribution, Hitting Time, First Step Equations | W 1, 2.4, 2.6, 13.3, B-T 7.1-7.4 Markov Chains |

10/13 | DTMCs: Reversibility, Infinite States, Classification, Big Theorem | Reversibility |

10/18 | DTMC Wrapup | B-T 6.1-6.3, W 13.4 |

10/20 | Poisson Processes: Counting Process, Memorylessness, Merging, Splitting | B-T 6.1-6.3, W 13.4 Poisson Process |

10/25 | PP: Erlang Distribution, Random Incidence | B-T 6.1-6.3, W 13.4 |

10/27 | Continuous Time Markov Chains: Rate Matrix and Stationary Distribution | B-T 7.5, W 13.5 |

11/01 | CTMCs: Big Theorem, First Step Equations and Jump Chain | B-T 7.5, W 13.5 CTMCS |

11/03 | No Lecture (Midterm) | |

11/08 | Erdos-Renyi Random Graphs | Random Graphs |

11/10 | Maximum Likelihood Estimation, Maximum a Posteriori Estimation | B-T 8.1-8.2, 9.1, W 5.1 |

11/15 | Statistical Hypothesis Testing, Neyman-Pearson Lemma | Hypothesis Testing B-T 9.3-9.4, W 5.5-5.6, 6.5 |

11/17 | Linear Least Square Estimate, Vector Space of Random Variables | Hilbert space of RVs B-T 8.3-8.5, W 7.1-7.5 |

11/22 | Minimum Mean Square Error Estimation | W 7.1-7.5, W 8.1 |

11/29 | Jointly Gaussian Random Variables | W 6.3-6.4, 7.6, 8.1-8.3 Jointly Gaussian RVs |

12/1 | Orthogonal Updates and Kalman Filter | W 7.6, 8.1-8.3 Kalman Filter (1) Kalman Filter (2) |