APPLIED PROBABILITY (MA 3014)

Fall 2020

The course is an introduction to probabililty from a mathematical perspective, including discrete and continous random variables, expectations and variances, limit theorems, etc. View the syllabus.

Mike O'Neil
(oneil@cims.nyu.edu)

Monday, Wednesday 2:00pm - 3:15pm

ONLINE

**Office hours**

Thursday 10:00am - 12:00pm

Join: nyu.zoom.us/my/mike.oneil

Haoxiang Huang (hh1987@nyu.edu)

Friday 2:00pm - 3:15pm

ONLINE

**Office hours**

Monday 3:30pm - 4:30pm

ONLINE

- This course will be run
**online**this semester due to COVID-19. - Please join the course page on Campuswire. Email the professor for the passcode.
- Activate your NYU sponsored account on Overleaf. You will use Overleaf to collaborate on lecture note preparation. I recommend going through the tutorial if you are new to Overleaf and/or LaTeX.

The main textbook for the course is Ross,
*A First Course in Probability*, 10th Ed., 2018.
An earlier edition of the textbook is available for free
via NYU libraries. It is not necessary to have the latest edition.

The final numerical grade will be computed basic on the following rubric:

10% | Engagement on Campuswire | |

15% | Preparation of lecture notes | |

15% | Quizzes (every other week) | |

20% | Exam 1 | |

20% | Exam 2 | |

20% | Exam 3 |

Below is an updated list of discussion topics along with any documents that were distributed, notes, or relevant code.

Date | Topics | Asynchronous | Synchronous |
---|---|---|---|

Sep 2 | Intro to the course, logistics | Zoom recording | |

Sep 7 | NO CLASS | ||

Sep 9 | Counting, permutations, combinations Ross 1.1-1.4 |
Lecture video Lecture notes Student notes |
Zoom recording Notes |

Sep 14 | Multinomial coefficients, sample spaces Ross 1.5, 2.1-2.2 |
Lecture video Lecture notes Student notes |
Zoom recording Notes |

Sep 16 | Axioms of probability, some propositions Ross 2.3-2.4 |
Lecture video Lecture notes Student notes |
Zoom recording Notes |

Sep 21 | Sample spaces with equally likely outcomes, probability as belief Ross 2.5, 2.7 |
Lecture video Lecture notes Student notes |
Zoom recording Notes |

Sep 23 | Conditional probability, Bayes' rule Ross 3.1-3.3 |
Lecture video Lecture notes Student notes |
Zoom recording Notes |

Sep 28 | Independent events Ross 3.4 |
Lecture video Lecture notes Student notes |
Zoom recording Notes |

Sep 30 | Conditional probably, again Ross 3.5 |
Lecture video Lecture notes Student notes |
Zoom recording Notes |

Oct 5 | Discrete random variables, expected value Ross 4.1-4.3 |
Lecture video Lecture notes Student notes |
Zoom recording Notes |

Oct 7 | Exam 1 | ||

Oct 12 | Expectations of functions of a RV; variance Ross 4.4-4.5 |
Lecture video Lecture notes Student notes |
Zoom recording Notes |

Oct 14 | Bernoulli and binomial random variables Ross 4.6 |
Lecture video Lecture notes |
Zoom recording Notes |

Oct 19 | Poisson random variables Ross 4.7 |
Lecture video Lecture notes Student notes |
Zoom recording Notes |

Oct 21 | Other discrete random variables, expectations of
sums Properties of the CDF Ross 4.8-4.10 |
Lecture video Lecture notes Student notes |
Zoom recording Notes |

Oct 26 | Continuous random variables Ross 5.1-5.2 |
Lecture video Lecture notes Student notes |
Zoom recording Notes |

Oct 28 |
Uniform and normal random variables Ross 5.3-5.4 |
Lecture video Lecture notes Student notes |
Zoom recording Notes |

Nov 2 |
Normal approximation to the binomial distribution Exponential, Gamma, and Cauchy distributions Ross 5.4.1, 5.5-5.6 |
Lecture video Lecture notes Student notes |
Zoom recording Notes |

Nov 4 | Functions of continuous random variables; joint
distributions Ross 5.7, 6.1 |
Lecture video Lecture notes Student notes |
Zoom Recording Notes |

Nov 9 |
Distribution of sums of independent random variables Ross 6.2-6.3 |
Lecture video Lecture notes Student notes |
Zoom Recording Notes |

Nov 11 | Exam 2 | ||

Nov 16 |
Conditional distributions Ross 6.4-6.5 |
Lecture video Lecture notes Student notes |
Zoom Recording Notes |

Nov 18 |
Order statistics; functions of several random
variables Ross 6.6-6.7 |
Lecture video Lecture notes Student notes |
Zoom Recording Notes |

Nov 23 | Expectations of sums, covariance, correlation Ross 7.1-7.2, 7.4 |
Lecture video Lecture notes Student notes |
Zoom Recording Notes |

Nov 25 |
Conditional expectation and prediction Ross 7.5-7.6 |
Lecture video Lecture notes Student notes |
Zoom Recording Notes |

Nov 30 |
Moment generating functions; properties of normal
variates Ross 7.7-7.8 |
Lecture video (Part I) Lecture video (Part II) Lecture notes Student notes |
Zoom Recording Notes |

Dec 2 |
Central Limit Theorem Ross 8.1-8.3 |
Lecture video Lecture notes Student notes |
Zoom Recording Notes |

Dec 7 |
Strong Law of Large Numbers, more inequalities Ross 8.4-8.5 |
Lecture video Lecture notes Student notes |
Zoom Recording Notes |

Dec 9 |
Poisson processes Ross 9.1 |
Lecture video Lecture notes |
Zoom Recording Notes |

Dec 18 | Final Exam, 2:00pm-3:50pm | ||