Section 001
Math 3160 — Probability (Syllabus Fall 2021)
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 30 — September 3):
- read Chapter 1 “Combinatorics”;
- optional: listen to Video Lectures 01a, 01b, 01c;
- do all exercises in this chapter (ask questions in class);
- Sample Quiz Chapter 1, solution 2019
- Sample Quiz Chapter 1, solution 2018
- Sample Quiz Chapter 1 with solution 2017
- Sample Quiz Chapter 1 with solution 2020
- 538 Riddler Express (AUG. 27, 2021) for extra credit (submit by email by Wednesday)
- look for current events: Hurricane Ida
- Quiz 1 Friday September 3 in class
HW 2 (September 6 — September 10):
- Review HW for week 1 and do any unfinished work;
- read Chapter 2 “The probability set-up”;
- optional: listen to Video Lectures 02a, 02b;
- do all exercises in this chapter (ask questions in class);
- Sample Quiz 2 with solution
- Sample Quiz Chapter 2, solution 2020
- Sample Quiz Chapter 2, solution 2019
- Sample Quiz Chapter 2, solution 2018
- Sample Quiz Chapter 2 with solution 2017
- Quiz 2 on Friday September 10 (solution)
HW 3 (September 13 — September 17):
- Review HW for week 2 and do any unfinished work;
- read Chapter 3 “Independence” and Chapter 4 “Conditional probability”;
- optional: listen to Video Lecture 3a for Chapter 3 and Video Lectures 3b and 3c for Chapter 4;
- ask questions in class;
- Quiz 3+4 on Friday September 17
- jhu.edu/testing-positivity
- Sample Quiz 3+4
- Sample Quiz Chapters 3+4, (with solution 2020):
- Sample Quiz Chapter 3 solution (2019)
- Sample Quiz Chapter 4 solution (2019)
- Sample Quiz Chapter 3 solution (2018)
- Sample Quiz Chapter 4 solution (2018)
- Sample Quiz Chapter 3 with solutions (2017)
- Sample Quiz Chapter 4 with solutions (2017)
HW 4 (September 21 — September 25):
- Review HW for week 3 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;
- Sample Quiz 5 with solution (2020 Fall)
- Sample Quiz 5 solution (2020 Spring)
- Sample Quiz 5 solution (2019)
- Sample Quiz 5 solution (2018)
- Sample Quiz 5 with solutions (2017)
- quiz 5 Fall 2021 (answers)
HW 5 (September 27 — October 1):
- read Chapter 6 “Some discrete distributions“;
- ask questions in class; quiz 6 answers
- How to pronounce Poisson? /ˈpwɑːsɒn/
- Matt Bognar’s applets for discrete distributions
- Geometric and Poisson distributions in infection spread (538 Riddler Classic solution and an article by Emma Knight)
- Sample Quiz 6 (Fall 2020);
- Sample Quiz 6 (Spring 2020), solution
- Sample Quiz Chapter 6 with solution (2019)
- Sample Quiz Chapter 6 with answers (2018)
- Sample Quiz Chapter 6 with solutions (2017)
HW 6 (October 4 — October 8):
- Review HW for the previous week and do any unfinished work;
- read Chapter 7 “Continuous distributions”;
- ask questions in class;
- Quiz on Friday October 8 (Chapters 6 and 7) Answers
- Sample Quiz Chapter 7 with solutions (Fall 2020);
- Sample Quiz Chapter 7 with solution (Spring 2020)
- Sample Quiz Chapter 7 with solution (2019)
- Sample Quiz Chapter 7 with answers (2018)
- Sample Quiz Chapter 7 with solutions (2017)
HW 7 (October 12 — October 15):
- Review HW for the previous week and do any unfinished work;
- read Chapter 8 “Normal distribution”.pdf and Chapter 9 “Normal approximation”.pdf;
- ask questions in class: normal-Gaussian.png and binomial.jpg
- Sample quiz 8-9 with solution (Fall 2020);
- Sample Quiz Chapters 8-9.pdf, with solution (Spring 2020)
- Sample Quiz Chapters 8-9.pdf with solutions (2019)
- Sample Quiz Chapters 8-9.pdf with solutions (2018)
- Sample Quiz Chapters 8-9 with solutions (2017)
- graphing applet for the binomial distribution
HW 8 (October 18 — October 22):
-
- Review HW for the previous week and do any unfinished work;
- try to solve the optional posted 538 Riddle for extra credit by Wednesday October 20;
- 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;
- ask questions in class;
- Sample Quiz Chapter 10 (2020);
- Sample Quiz Chapter 10 and solution (2019)
- Sample Quiz Chapter 10 and solution (2018)
- Sample Quiz Chapter 10 and solutions (2017) with notes
- a sample Test 2a with answers (2017a)
- a sample Test 2b with solutions (2017b) with notes
HW 9 (October 25 — October 29)
- Review HW for the previous week and do any unfinished work;
- read Chapter 11 “Multivariate distributions“; do all exercises;
- Quiz 11 on Friday October 29;
- Sample Quiz Chapter 11 (Fall 2020);
- Sample Quiz Chapter 11 (Spring 2020), solution
- Sample Quiz Chapter 11 and solution (2019)
- Sample Quiz Chapter 11 and solution (2018)
HW 10 (November 1 — November 5)
- Review HW for the previous week and do any unfinished work;
- read Chapter 12 “Expectations” and do all examples and exercises;
- ask questions (here are pictures from the white board, November 26, 2018 and November 19, 2019; white board 2020-11-02 )
- Sample Quiz 12 (Fall 2020);
- Sample Quiz Chapter 12, solution (Spring 2020)
- Sample Quiz Chapter 12 and solution (2019)
- Quiz Chapters 11-12 with solutions (2017)
- Sample Test 2 with answers (2018)
HW 11 (November 8 — November 12)
- Review HW for the previous week and do any unfinished work;
- read Chapter 13 “Moment generating functions” (do all examples and exercises);
- white board 2020-11-09 ;
- Quiz on Chapter 13 on Friday November 12;
- Sample Quiz on Chapter 13 (Fall 2020);
- Sample Quiz on Chapter 13 (Spring 2020) notes hints solution
- Sample Quiz Chapters 12-13 and answers (2018)
- Sample Quiz Chapters 13-14, mostly based on Chapters 13 and 14 with some questions coming from chapters 8, 9, 10, 11, 12. solution (2019)
- Quiz Chapters 13-14 with solutions (2017).
- ask questions by email
HW 12 (November 15 — November 19)
- Review HW for the previous week and do any unfinished work;
- read Chapter 14 “Limit laws” (do all examples and exercises);
- optional: listen to Video Lectures 8a and 8b for Chapter 14;
- Quiz Chapter 14 on Friday November 19 (either in-class or take-home version);
- Sample quizzes for Chapter 14: in-class and take-home versions;
- ask questions (here are pictures from the white board, December 5, 2018);
- Sample Quiz Chapter 14 solution 2020
- Sample Quiz Chapter 14, mostly based on Chapter 14 with some questions coming from chapters 8, 9, 10, 11, 12, 13. answers (2018)
HW 14 (December 6 — December 10)
- read Chapter 15 “Probability inequalities”, focus on Markov’s and Chebyshev’s inequalities;
- read Chapter 16 “Applications in Insurance and Actuarial Science”, focus on 16.2, 16.4, 16.5;
- Quiz on Chapters 15 and 16 on Friday December 10
Final Exam (optional) 12/17/21 8:00 am – 10:00 am MONT 110
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