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 setup”;
 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/testingpositivity
 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: normalGaussian.png and binomial.jpg
 Sample quiz 89 with solution (Fall 2020);
 Sample Quiz Chapters 89.pdf, with solution (Spring 2020)
 Sample Quiz Chapters 89.pdf with solutions (2019)
 Sample Quiz Chapters 89.pdf with solutions (2018)
 Sample Quiz Chapters 89 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 20201102 )
 Sample Quiz 12 (Fall 2020);
 Sample Quiz Chapter 12, solution (Spring 2020)
 Sample Quiz Chapter 12 and solution (2019)
 Quiz Chapters 1112 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 20201109 ;
 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 1213 and answers (2018)
 Sample Quiz Chapters 1314, mostly based on Chapters 13 and 14 with some questions coming from chapters 8, 9, 10, 11, 12. solution (2019)
 Quiz Chapters 1314 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 inclass or takehome version);
 Sample quizzes for Chapter 14: inclass and takehome 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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