Section 001
Math 3160 — Probability (Syllabus Fall 2021.pdf)
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”.pdf;
- optional: listen to Video Lectures 01a, 01b, 01c;
- do all exercises in this chapter (ask questions in class);
- Sample Quiz Chapter 1.pdf, solution 2019.pdf
- Sample Quiz Chapter 1.pdf, solution 2018.pdf
- Sample Quiz Chapter 1 with solution 2017.pdf
- Sample Quiz Chapter 1 with solution 2020.pdf
- 538 Riddler Express (AUG. 27, 2021) for extra credit (submit by email by Wednesday)
- look for current events: Hurricane Ida
- Quiz 1.pdf 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”.pdf;
- optional: listen to Video Lectures 02a, 02b;
- do all exercises in this chapter (ask questions in class);
- Sample Quiz 2 with solution.pdf
- Sample Quiz Chapter 2.pdf, solution 2020.pdf
- Sample Quiz Chapter 2.pdf, solution 2019.pdf
- Sample Quiz Chapter 2.pdf, solution 2018.pdf
- Sample Quiz Chapter 2 with solution 2017.pdf
- Quiz 2.pdf on Friday September 10 (solution.jpg)
HW 3 (September 13 — September 17):
- Review HW for week 2 and do any unfinished work;
- read Chapter 3 “Independence”.pdf and Chapter 4 “Conditional probability”.pdf;
- 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.pdf on Friday September 17
- jhu.edu/testing-positivity
- Sample Quiz 3+4.pdf
- Sample Quiz Chapters 3+4.pdf, (with solution 2020).pdf:
- Sample Quiz Chapter 3.pdf solution (2019).pdf
- Sample Quiz Chapter 4.pdf solution (2019).pdf
- Sample Quiz Chapter 3.pdf solution (2018).pdf
- Sample Quiz Chapter 4.pdf solution (2018).pdf
- Sample Quiz Chapter 3 with solutions (2017).pdf
- Sample Quiz Chapter 4 with solutions (2017).pdf
HW 4 (September 21 — September 25):
- Review HW for week 3 and do any unfinished work;
- read Chapter 5 “Random variables”.pdf;
- optional: listen to Video Lectures 4a and 4b for Chapter 5;
- ask questions in class;
- Sample Quiz 5 with solution (2020 Fall).pdf
- Sample Quiz 5.pdf solution (2020 Spring).pdf
- Sample Quiz 5.pdf solution (2019).pdf
- Sample Quiz 5.pdf solution (2018).pdf
- Sample Quiz 5 with solutions (2017).pdf
- quiz 5 Fall 2021.pdf (answers.pdf)
HW 5 (September 27 — October 1):
- read Chapter 6 “Some discrete distributions.pdf“;
- ask questions in class; quiz 6 answers.pdf
- 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.pdf)
- Sample Quiz 6 (Fall 2020).pdf;
- Sample Quiz 6 (Spring 2020).pdf, solution.pdf
- Sample Quiz Chapter 6.pdf with solution (2019).pdf
- Sample Quiz Chapter 6.pdf with answers (2018).pdf
- Sample Quiz Chapter 6 with solutions (2017).pdf
HW 6 (October 4 — October 8):
- Review HW for the previous week and do any unfinished work;
- read Chapter 7 “Continuous distributions”.pdf;
- ask questions in class; .pdf
- Quiz.pdf on Friday October 8 (Chapters 6 and 7) Answers.pdf
- Sample Quiz Chapter 7 with solutions (Fall 2020).pdf;
- Sample Quiz Chapter 7.pdf with solution (Spring 2020).pdf
- Sample Quiz Chapter 7.pdf with solution (2019).pdf
- Sample Quiz Chapter 7.pdf with answers (2018).pdf
- Sample Quiz Chapter 7 with solutions (2017).pdf
HW 7 (October 12 — October 15):
- Review HW for the previous week and do any unfinished work;
- read Chapter 8 “Normal distribution”.pdf.pdf and Chapter 9 “Normal approximation”.pdf.pdf;
- ask questions in class: normal-Gaussian.png.png and binomial.jpg.jpg
- Sample quiz 8-9 with solution (Fall 2020).pdf;
- Sample Quiz Chapters 8-9.pdf.pdf, with solution (Spring 2020).pdf
- Sample Quiz Chapters 8-9.pdf.pdf with solutions (2019).pdf
- Sample Quiz Chapters 8-9.pdf.pdf with solutions (2018).pdf
- Sample Quiz Chapters 8-9 with solutions (2017).pdf
- 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.pdf;
- read and memorize Strategy to transform continuous random variables.pdf and this table of continuous distributions.pdf;
- ask questions in class;
- Sample Quiz Chapter 10.pdf (2020);
- Sample Quiz Chapter 10.pdf and solution (2019).pdf
- Sample Quiz Chapter 10.pdf and solution (2018).pdf
- Sample Quiz Chapter 10.pdf and solutions (2017).pdf with notes.pdf
- a sample Test 2a.pdf with answers (2017a).pdf
- a sample Test 2b.pdf with solutions (2017b).pdf with notes.pdf
HW 9 (October 25 — October 29)
- Review HW for the previous week and do any unfinished work;
- read Chapter 11 “Multivariate distributions.pdf“; do all exercises;
- Quiz 11 on Friday October 29;
- Sample Quiz Chapter 11.pdf (Fall 2020);
- Sample Quiz Chapter 11 (Spring 2020).pdf, solution.pdf
- Sample Quiz Chapter 11.pdf and solution (2019).pdf
- Sample Quiz Chapter 11.pdf and solution (2018).pdf
HW 10 (November 1 — November 5)
- Review HW for the previous week and do any unfinished work;
- read Chapter 12 “Expectations”.pdf and do all examples and exercises;
- ask questions (here are pictures from the white board, November 26, 2018 and November 19, 2019.jpg; white board 2020-11-02 )
- Sample Quiz 12.pdf (Fall 2020);
- Sample Quiz Chapter 12.pdf, solution.pdf (Spring 2020)
- Sample Quiz Chapter 12.pdf and solution (2019).pdf
- Quiz Chapters 11-12 with solutions (2017).pdf
- Sample Test 2.pdf with answers (2018).pdf
HW 11 (November 8 — November 12)
- Review HW for the previous week and do any unfinished work;
- read Chapter 13 “Moment generating functions.pdf” (do all examples and exercises);
- white board 2020-11-09 ;
- Quiz on Chapter 13 on Friday November 12;
- Sample Quiz on Chapter 13.pdf (Fall 2020);
- Sample Quiz on Chapter 13.pdf (Spring 2020) notes.pdf hints.pdf solution.pdf
- Sample Quiz Chapters 12-13.pdf and answers (2018).pdf.pdf
- Sample Quiz Chapters 13-14.pdf, mostly based on Chapters 13 and 14 with some questions coming from chapters 8, 9, 10, 11, 12. solution (2019).pdf
- Quiz Chapters 13-14 with solutions (2017)..pdf
- 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”.pdf (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.pdf and take-home.pdf versions;
- ask questions (here are pictures from the white board, December 5, 2018);
- Sample Quiz Chapter 14.pdf solution 2020.pdf
- Sample Quiz Chapter 14,.pdf mostly based on Chapter 14 with some questions coming from chapters 8, 9, 10, 11, 12, 13. answers (2018).pdf
HW 14 (December 6 — December 10)
- read Chapter 15 “Probability inequalities”.pdf, focus on Markov’s and Chebyshev’s inequalities;
- read Chapter 16 “Applications in Insurance and Actuarial Science”.pdf, 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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