Section 001
Math 3160 — Probability (Syllabus Fall 2020)
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 31 — September 4):
 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
 quiz 1 Friday September 4 solution 2020
HW _{2} (September 7 — September 11):
 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);
 Quiz 2 on Friday September 11 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
HW _{3} (September 14 — September 18):
 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;
 try to solve the optional posted riddle for extra credit by Wednesday September 16;
 ask questions in class;
 Quiz 3+4 on Friday September 18 jhu.edu/testingpositivity
 Sample Quiz Chapters 3+4, based on Chapters 3 and 4 (with solution):
 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;
 Quiz 5 on Friday September 25;
 Sample Quiz Chapter 5, based on Chapter 5 (with solution):
 Sample Quiz Chapter 5 solution (2019)
 Sample Quiz Chapter 5 solution (2018)
 Sample Quiz Chapter 5 with solutions (2017)
HW _{5} (September 28 — October 2):
 read Chapter 6 “Some discrete distributions“;
 optional: listen to Video Lectures 4c and 4d for Chapter 6;
 ask questions in class;
 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)
 Quiz 6 on Friday October 2;
 Sample Quiz Chapter 6, 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 5 — October 9):
 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 Friday October 9;
 Sample Quiz Chapter 7, based on Chapter 7. solution
 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;
 try to solve the optional posted riddle for extra credit by Wednesday October 14;
 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: normalGaussian and binomial
 Quiz 89 on Friday October 16;
 Sample Quiz Chapters 89, based on Chapters 8 and 9. solution
 Sample Quiz Chapters 89 with solutions (2019)
 Sample Quiz Chapters 89 with solutions (2018)
 Sample Quiz Chapters 89 with solutions (2017)
 graphing applet for the binomial distribution
HW _{8} (October 19 — October 23):
 Review HW for the previous week and do any unfinished work;
 try to solve the optional posted riddle for extra credit by Wednesday October 21;
 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 Friday October 23;
 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 26 — October 30)
 Review HW for the previous week and do any unfinished work;
 try to solve the optional posted riddle for extra credit by Wednesday October 28;
 Quiz 11 on Friday October 30;
 read Chapter 11 “Multivariate distributions“; do all exercises;
 optional: listen to Video Lectures 6a, 6b, 6c and 6d, for Chapter 11;
 ask questions by email;
 Sample Quiz Chapter 11, solution
 Sample Quiz Chapter 11 and solution (2019)
 Sample Quiz Chapter 11 and solution (2018)
HW _{10} (November 2 — November 6)
 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 (here are pictures from the white board, November 26, 2018 and November 19, 2019; white board 20201102 )
 Quiz 12 on Friday November 6;
 Sample Quiz Chapter 12, solution
 Sample Quiz Chapter 12 and solution (2019)
 Quiz Chapters 1112 with solutions (2017)
 Sample Test 2 with answers (2018)
HW _{11} (November 9 — November 13)
 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 ;
 optional: listen to Video Lectures 7d and 7e for Chapter 13;
 Quiz Chapter 13 on Friday November 13;
 Sample Quiz Chapter 13 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 16 — November 20)
 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 20 (either inclass or takehome version);
 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)
Take home test December 3–6 (Thursday — Sunday)
 Sample Test 1 from Spring 2020, based on Chapters 1, 2, 3, 4, 5. solution
 Sample Test 1, solution (2019)
 Sample Test 1 with solutions (2018)
 Sample Test 1 with solutions (2017)
 extra problems with solutions
 Sample Test 2 (from Spring 2020)
 notes
 solution
 mostly based on Chapters 11 and 12 with some questions coming from chapters 1–10
 extra sample Test 2 problems; with answers (2018)
 sample final exam problems and answers (2018)
 9 sample final exam questions with answers (2017)
 10 sample final exam questions with answers (2017)
Final Exam:

takehome openbook Final Exam: from Thursday December 17 to Sunday December 20
 office hour time for the final exam:
12/18/2020, Friday8:00AM – 10:00AM