Section 006
Math 3160 — Probability (Syllabus Fall 2019)
Catalog description: Introduction to the theory of probability. Sets and counting, probability axioms, conditional probabilities, random variables, limit theorems. Three credits. Prerequisite: MATH 2110Q, 2130Q or 2143Q.
Open source educational materials are provided (no textbook is necessary for this course)
Standard syllabus for Math 3160 Probability:
- Combinatorics: product rule and permutations; combinations.
- Axioms of Probability: sample spaces, events and set operations; probability axioms.
- Conditional Probability and Independence: conditional probability and Bayes rule; probability trees; independent events.
- Discrete Random Variables: probability mass function (PMF), cumulative distribution function (CDF); expectation; variance, moments, moment generating function (MGF). Uniform, Bernoulli, Binomial, Poisson, Geometric, Hypergeometric distributions; expectation, variance, MGF of these RVs.
- Continuous Univariate Random Variables: probability density function (PDF), CDF, expectation, variance, moments, MGF. Uniform, Exponential, Gamma, Normal distributions; expectation, variance, MGF of these RVs. Transformations (functions) of continuous RVs.
- Jointly Distributed Random Variables: joint PMF/PDF, and CDF; marginal distributions; conditional PMF/PDF; conditional expectation and variance; covariance and correlation coefficients.
- Limit Theorems: Weak Law of Large Numbers, Central Limit Theorem, Normal approximations.
HW 1 (August 26 — August 30):
- read Chapter 1 “Combinatorics”;
- optional: listen to Video Lectures 01a, 01b, 01c;
- do all exercises in this chapter (ask questions in class);
- Quiz 1 on Thursday August 29. solution
HW 2 (September 2 — September 6):
- Review HW for week 1 and do any unfinished work;
- read Chapter 2 “The probability set-up” (you can skip the exercises, focus on Subsection 2.1. Introduction and basic theory);
- optional: listen to Video Lectures 02a, 02b;
- ask questions in class;
- Quiz 2 on Thursday September 5, based on Chapter 1 and Subsection 2.1. solution
HW 3 (September 9 — September 13):
- Review HW for week 2 and do any unfinished work;
- read Chapter 2 “The probability set-up” and Chapter 3 “Independence”;
- optional: listen to Video Lecture 3a for Chapter 3;
- ask questions in class;
- Quiz 3 on Thursday September 12, based on Chapters 2 and 3. solution
HW 4 (September 16 — September 20):
- Review HW for week 3 and do any unfinished work;
- read Chapter 4 “Conditional probability”;
- optional: listen to Video Lectures 3b and 3c for Chapter 4;
- ask questions in class;
- Quiz 4 on Thursday September 19, based on Chapter 4. solution
HW 5 (September 23 — September 27):
- Review HW for week 4 and do any unfinished work;
- read Chapter 5 “Random variables”;
- optional: listen to Video Lectures 4a and 4b for Chapter 5;
- ask questions in class;
- Quiz 5 on Thursday September 26, based on Chapter 5. solution
HW 6 (September 30 — October 4):
- Review HW for weeks 1, 2, 3, 4, 5 and do any unfinished work;
- ask questions in class on Tuesday;
- Test 1 on Thursday October 3, based on Chapters 1, 2, 3, 4, 5. solution
You are allowed to bring 1 page of handwritten notes (both sides of an 8 x 11 paper).
HW 7 (October 7 — October 11):
- Review Test 1, do any unfinished work;
- read Chapter 6 “Some discrete distributions“;
- optional: listen to Video Lectures 4c and 4d for Chapter 6;
- ask questions in class;
- Quiz 6 on Thursday October 10, based on Chapter 6. solution
HW 8 (October 14 — October 18):
- Review HW for the previous week and do any unfinished work;
- read Chapter 7 “Continuous distributions”;
- optional: listen to Video Lectures 5a for Chapter 7;
- ask questions in class;
- Quiz 7 on Thursday October 17, based on Chapter 7. solution
HW 9 (October 21 — October 25):
- Review HW for the previous week and do any unfinished work;
- read Chapter 8 “Normal distribution” and Chapter 9 “Normal approximation”;
- optional: listen to Video Lecture 5b for Chapters 8 and 9;
- ask questions in class: normal-Gaussian and binomial
- Quiz 8-9 on Thursday October 24, based on Chapters 8 and 9. solution
HW 10 (October 28 — November 1):
- Review HW for the previous week and do any unfinished work;
- read Chapter 10 “Some continuous distributions” and do all exercises;
- read and memorize Strategy to transform continuous random variables and this table of continuous distributions;
- optional: listen to Video Lectures 5c and 5d for Chapter 10;
- ask questions in class;
- Quiz 10 on Thursday October 31, based on Chapter 10. solution
HW 11 (November 4 — November 8):
- Review HW for the previous week and do any unfinished work;
- read Chapter 11 “Multivariate distributions“; do all exercises;
- optional: listen to Video Lectures 6a, 6b, 6c and 6d, for Chapter 11;
- ask questions in class;
- Quiz 11 on Thursday November 7, based on Chapter 11. solution
HW 12 (November 11 — November 15):
- Review HW for weeks 7, 8, 9, 10, 11 and do any unfinished work;
- ask questions in class on Tuesday;
- sample Test 2 problems; with answers (here are pictures from the white board);
- review session on Wednesday November 13, 7pm-8pm, MONT 214;
- Test 2 on Thursday November 14, based on Chapters 6, 7, 8, 9, 10, 11. solution
- You are allowed to bring 2 pages of handwritten notes (both sides of an 8 x 11 paper). Table of distributions and Z-table from the end of the textbook will be provided.
HW 13 (November 18 — November 22):
- Review HW for the previous week and do any unfinished work;
- read Chapter 12 “Expectations” and do all examples and exercises;
- optional: listen to Video Lectures 7a, 7b, 7c for Chapter 12;
- ask questions in class (here are pictures from the white board, November 26, 2018 and November 19, 2019);
- Quiz 12 on Thursday November 21, based on Chapters 11, 12. solution
HW 14 (Thanksgiving and December 2 — December 6):
- Review HW for the previous week and do any unfinished work;
- read Chapter 13 “Moment generating functions” and Chapter 14 “Limit laws” (do all examples and exercises);
- optional: listen to Video Lectures 7d and 7e for Chapter 13 and Video Lectures 8a and 8b for Chapter 14; ask questions in class (here are pictures from the white board, December 5, 2018);
- Quiz 13-14 on Thursday December 5, mostly based on Chapters 13 and 14 with some questions coming from chapters 8, 9, 10, 11, 12. You are allowed to bring 3 pages of handwritten notes (both sides of an 8 x 11 paper). solution
Review session: MONT 320 on Sunday, December 8th 2pm–4 pm, to discuss sample final exam problems (here are answers) and any other questions
Final exam:
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12/9/2019, Monday
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3:30PM – 5:30PM
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- You are allowed to bring 3 pages of handwritten notes (both sides of an 8 x 11 paper). Table of distributions and Z-table from the end of the textbook will be provided if needed.