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 set-up”;
- 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/testing-positivity
- 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: normal-Gaussian and binomial
- Quiz 8-9 on Friday October 16;
- Sample Quiz Chapters 8-9, based on Chapters 8 and 9. solution
- Sample Quiz Chapters 8-9 with solutions (2019)
- Sample Quiz Chapters 8-9 with solutions (2018)
- Sample Quiz Chapters 8-9 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 2020-11-02 )
- Quiz 12 on Friday November 6;
- Sample Quiz Chapter 12, solution
- Sample Quiz Chapter 12 and solution (2019)
- Quiz Chapters 11-12 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 2020-11-09 ;
- 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 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 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 in-class or take-home 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:
-
take-home open-book Final Exam: from Thursday December 17 to Sunday December 20
- office hour time for the final exam:
12/18/2020, Friday8:00AM – 10:00AM