# Probability and Random Processes

Spring 2024

Jiantao
Jiao

Lecture: Tue & Thu 2:00 pm - 3:30 pm, Physics Building 4

Office Hour: Tue 4:00 pm - 5:00 pm, Cory 212

## Announcements

- Welcome to EECS 126! Please read the course info for logistics. We will be syncing Ed with the course roster periodically. If you are newly enrolled but not added to Ed after a few days, please email eecs126-spr24@lists.eecs.berkeley.edu and provide your student ID. We will use Gradescope for all submissions/grade-related items. If you are not added automatically, please use the code 4GZG68 to join.
- Time conflicts are allowed only if you choose to attend EECS 126 lectures. The lectures are not recorded and midterms will be held during lecture times. There will be no alternative 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 |
---|---|---|

1/16 | Introduction, Probability Spaces, Conditional Probability Theorem | BT 1.1-1.3 |

1/18 | Law of Total Probability, Bayes' Rule, Independence | BT 1.4, 1.5 |

1/23 | Discrete Random Variables: Bernoulli, Binomial, Geometric and Poisson Variables | BT 2.1-2.3 |

1/25 | Expectation, Variance, Conditional Expectation | BT 2.4-2.6 |

1/30 | Continuous Random Variables: Uniform, Exponential Variables | BT 3.1, 3.2 |

2/1 | Normal Random Variables, Multiple Random Variables, Conditioning | BT 3.3-3.5 |

2/6 | Continuous Bayes, Derived Distributions | BT 3.6, 4.1 |

2/8 | Covariance, Law of Iterated Expectation, Law of Total Variance | BT 4.2-4.3 |

2/13 | Moment Generating Function, Sum of Random Variables | BT 4.4-4.6 |

2/15 | Multivariate Gaussian, Concentration Inequalities, Weak Law of Large Numbers | Multivariate
Gaussian BT 5.1, 5.2 |

2/20 | Convergence in Probability, Distribution and Expectation | Convergence |

2/22 | No Lecture | |

2/27 | Midterm 1 | |

2/29 | Central Limit Theorem, Strong Law of Large Numbers | BT 5.4-5.6, W 2.3, 3.2, 4.2 |

3/5 | Discrete Time Markov Chains, States Classification | BT 7.1, 7.2 |

3/7 | DTMCs: Stationary Distribution, Hitting Time | BT 7.3, 7.4, W 1.5 |

3/12 | DTMCs: Reversibility, Big Theorem | W 1.3, 2.5 Reversibility |

3/14 | Poisson Processes: Counting Process, Memorylessness, Splitting and Merging | DTMC_review BT 6.1, 6.2 |

3/19 | Poisson Processes: Erlang Distribution, Random Incidence | BT 6.2 |

3/21 | Continuous Time Markov Chains: Rate Matrix and Stationary Distribution | CTMCS BT 7.5, W 6.2 |

3/26 | Spring Break | |

3/28 | Spring Break | |

4/2 | MT2 Review | |

4/4 | Midterm 2 | |

4/9 | CTMCs: Big Theorem, Jump Chain and Kolmogorov Equation | CTMCS BT 7.5, W 6.2 |

4/11 | Bayesian Inference | BT 8.1 |

4/16 | Maximum a Posteriori Probability | BT 8.2 |

4/18 | Minimum Mean Square Error Estimate, Orthogonality, MMSE for Gaussian | BT 8.3, W 9.6 |

4/23 | Linear Least Square Estimate | BT 8.4, 8.5, W 9.3 |

4/25 | Maximum Likelihood Estimation, Linear Regression | BT 9.1, 9.2, W 7.2, 9.4, 9.5 |