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Spring, 2021
Ipython Notebook Markdown Bullets
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Ipython Notebook Markdown
Date | Readings and Resources | Homeworks/Labs | |||
| 0 | Th 1/29 | Administrative matters; Goals of the course; Motivating Examples: Why should you know probability and statistics? Probability and Statistics as the science of quantifying uncertainty. What is randomness? Lecture Slides: PDF | Required Reading: Textbook §1.1 Optional: Here is a nice exploration of the nature of randomness and our perceptions: HTML Just for Fun: Here is a short YT video with various clips from movies which involve probability (we will return to the Monty Hall Problem, the first clip, soon): YT For a wonderful and informative video by an expert mathematician about randomness and cards, see the YouTube video here. | Python Resources CS 237: HTML Summary of Python (with examples) for CS 237: IPYNB, ZIP HW 01: IPYNB, ZIP HW 01 Solution: IPYNB, ZIP | |
| 1 | T 2/2 | Basic definitions of probability theory: outcomes, sample spaces, probability functions, axioms for probability functions. Lecture 01: PDF | Required Reading: Textbook §1.3.1, 1.3.2 Review §1.2 as needed for math background. Optional (on infinite sets and countability): Math for Computer Science, § 7.1, p.192. Proof that reals are not countable: YT | Textbook practice problems (Optional but recommended): P1 - P5 | |
| 2 | Th 2/4 | Set operations on events and axiomatic method for proving theorems about probability functions;Axioms continued; Examples of finite, countably infinite, and uncountable sample spaces and typical problems in each. Probability functions for finite, equiprobable spaces, and extension to uncountable case. Anomalies arising from infinite sample spaces. Lecture 02: PDF | Required Reading: Textbook § 1.3.3 - 1.3.4 YouTube Video about axiomatic proofs: YT | Textbook practice problems (Optional but recommended): P1 - P5 | Markdown Tutorial: IPYNB HW 02: IPYNB, ZIP HW 02 Solution: PDF |
| 3 | T 2/9 | Non-Equiprobable sample spaces; Problem solving strategies; analysis using tree diagrams and the 'Four Step Method'; the Inverse Method. If time: The Monty Hall Problem. Lecture 03: PDF | Required Reading: Math for Computer Science, § 16.1 & § 16.2 on the 'Monty Hall Problem' and the 'Four Step Method. Optional: Look at the link above for a video of the 'Monty Hall Problem' from the movie 21 (featuring Kevin Spacey in better times); the scene shown was filmed in the CAS building. | ||
| 4 | Th 2/11 | Conditional Probability and Introduction to Independence Lecture Slides: PDF | Required: § 1.4.0 -- 1.4.1 Optional: Wikipedia on the Base Rate Fallacy: HTML | Textbook practice problems (Optional but recommended): P1 - P8 | HW 03: IPYNB, ZIP HW 03 Solution: PDF |
| T 2/16 | No Class: Monday Schedule | ||||
| 5 | Th 2/18 | Independence, Conditional Independence, and Bayes Rule Lecture Slides: PDF | Required: textbook § 1.4.2 - 1.4.4 | HW 04: IPYNB, ZIP HW 04 Solution: PDF | |
| 6 | T 2/23 | Counting principles and combinatorics; counting as sampling and constructing outcomes. Selection with and without replacement; permutations; counting sets vs sequences; the Unordering Principle; overcounting due to duplicates, multinomial coefficients. Lecture Slides: PDF | Required: Read Chapter 2 up through 2.1.2 Also, review the Inclusion/Exclusion Principle in section 1.3.3. | ||
| 7 | Th 2/25 | Combinations and 'N choose K'; Applications to probability problems. Poker hands will be used to illustrate these counting principles. Lecture Slides: PDF | Required: Read 2.1.3 up to Bernoulli Trials up through 2.1.2 Optional: Secrets of Pascal's Triangle Optional: This Wiki article section on 5-card poker is very good; | HW 05: IPYNB, ZIP HW 05 Solution: PDF | |
| 8 | T 3/2 | Poker Probability continued; Using combinations to count partitions; ordered partitions vs. unordered partitions; overcounting due to duplicates among subsets. Lecture Slides: PDF | No new reading MCS § 14.5 concerns powersets and counting subsets; ; Here is a nice explanation about how to count partitions, with intuitive examples. | ||
| 9 | Th 3/4 | Combinatorics and Finite Probability concluded; Choosing Multisets without Replacement Lecture Slides: PDF | HW 06: IPYNB, ZIP HW 06 Solution: PDF | ||
| 10 | T 3/9 | Discrete Random Variables; Functions and Expressions of RVs; Functions and expressions of random variables; (if time) independent and conditional random variables Lecture Slides: PDF | Required: 3.1.1 - 3.1.4. (you do not need to read about the hypergeometric, or the Poisson (yet)) For an illustration of the Binomial, take a look at this Quincunx animation: HTML | Textbook practice problems (optional but recommended): Ch. 3.1, Problems 1 -- 4 | |
| 11 | Th 3/11 | Finish independent and conditional RVs; Discrete Distributions: Bernoulli, Binomial, Geometric, and Pascal (Negative Binomial); Cumulative Distribution Functions Lecture Slides: PDF | Required: 3.1.5 Distributions Notebook: IPYNB, ZIP | HW 07: IPYNB, ZIP Solution: PDF | |
| 12 | T 3/16 | Finish Standard Discrete Distributions, memory-less property of Geometric; Introduction to Games and Expectation of RVs Lecture Slides: PDF | Required: 3.2.1-3.2.2 The Wiki article on the memoryless property is good, especially the examples on Waiting Times: HTML | Textbook practice problems (Optional but recommended): Ch. 3.2, Problems 1 - 3 | |
| Th 3/18 | No Lecture: BU Wellness Day | ||||
| F 3/19 | No Lab; Midterm Review Video and Sample Tests | Directory of past midterm solutions: DIR Sample problems and solutions on combinatorics: PDF Sample problems and solutions on basic probability: PDF Sample problems and solutions on conditional probability and independence: PDF | |||
| T 3/23 | Midterm Midterm Solution: PDF | ||||
| 13 | Th 3/25 | Expectation of RVs concluded; properties of expectation; expectation of special distributions Lecture Slides: PDF | Required: 3.2.2 (on expectation) Reading for the lab: OOP in Python | HW 08: IPYNB, ZIP HW 08 Solution: PDF | |
| 14 | T 3/30 | Expectation, Variance, Limit Theorems Lecture Slides: PDF | Required: 3.2.4 | ||
| 15 | Th 4/1 | Continuous Random Variables; the Normal Distribution Lecture Slides: PDF Brief video on integration for CS 237: YT | Required (continuous distributions): 4.1.0 - 4.2.1, and 4.2.3 | Textbook practice problems (Optional but recommended): Problems 1, 3, 4 | HW 09: IPYNBZIP HW 09 Solution: PDF |
| 16 | T 4/6 | Normal Distribution and the Normal approximation to the Binomial; the Continuity Correction Lecture Slides: PDF | Required (special continuous distributions): 4.2.3 | ||
| 17 | Th 4/8 | Central Limit Theorem and its Applications: Sampling Lecture Slides: PDF Jupyter notebook on CLT IPYNBZIP | HW 10: IPYNB, ZIP Solution: PDF | ||
| 18 | T 4/13 | Statistics as Applications of the CLT: Confidence Intervals Lecture Slides: PDF | Nice intro talk on : statistics in Python | ||
| 19 | Th 4/15 | Hypothesis Testing Lecture Slides: PDF | HW 11: IPYNB, ZIP | ||
| 20 | T 4/20 | Poisson Process: Counting processes, Poisson (Discrete) Distribution, relationship between Poisson and Exponential. Applications to Waiting Time problems and analysis of queues. Lecture Slides: PDF | Optional: A fun blog post about waiting times: HTML Optional: Here is the New Yorker article about earthquakes in the Pacific Northwest. Not-so-fun facts: (1) 'the Pacific Northwest has experienced forty-one subduction-zone earthquakes in the past ten thousand years. If you divide ten thousand by forty-one, you get two hundred and forty-three,' which is the mean; and (2) the last subduction-zone earthquake was in 1700, or 320 years ago. | ||
| 21 | Th 4/22 | Joint Random Variables; Independence, Covariance, and Correlation Lecture Slides: PDF | Chapter 5.1.1, 5.1.3 For continuous joint random variables, this is a reasonable introduction to the main points: HTML | HW 12: IPYNB, ZIP | |
| 22 | T 4/27 | Linear Regression: Least Squares Solutions, Linear Models Lecture: PDF Notebook with Examples: IPYNB | Chapter 8.5 | ||
| 23 | Th 4/29 | Multiple Regression, Machine Learning Lecture Slides: A, B | For Multiple Regression, I will follow fairly closely the treatment in sections 5.1 - 5.4 in this link. | ||
| T 5/4 | Final Exam from 3 - 5pm | Final Exam | Table for standard normal distribution (will be provided on exam): PDF Distributions Cheatsheet (will be provided on exam): PDF | Directory of Past Exams: DIR Practice Final Exam: IPYNB Practice Final Exam:DOCX Practice Final Exam:PDF Practice Final Exam Solution:PDF |