MATH 361 Introduction to Probability (Summer 2021)

Instructor: Yevgeniy Kovchegov

e-mail: kovchegy @math. oregonstate.edu

Office Hours: by appointment, via Zoom

Meets: live via Zoom MWF 4:00 pm - 5:20 pm, or prerecorded.

Grading scheme: Homework 60% and Online quizzes 40%

Textbooks:
(1) Charles M. Grinstead and J. Laurie Snell, Introduction to Probability available as a FREE e-book at http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html
A hard copy of the textbook can be acquired at bookstores such as Amazon.

(2) Mark Huber, Probability: Lectures and Labs available as a FREE e-book at https://www.markhuberdatascience.org/probability-textbook
A hard copy of the textbook can be acquired at bookstores such as Amazon.

Learning goals: MTH 361 moves at a fast pace from day one. We will concentrate on probability problem solving using concepts developed in calculus. Topics include probability models, discrete and continuous random variables, expectation and variance, the law of large numbers, and the central limit theorem.

Prerequisites: MTH 253 or MTH 306 or MTH 265, each, with a minimum grade of C-.

Syllabus: PDF

Quizzes and Homework: The homework assignments will need to be submitted in PDF format. The online quizzes will be offered on Canvas.

Schedule:
Monday, June 21 Introduction. Counting: Multiplicative rule of counting. Permutations. Combinations. Examples. Grinstead and Snell: Sections 3.1 and 3.2 Lectures 1-3 slides (PDF)
Wednesday, June 23 Combinations. Generalized combinations. Pascal's triangle. Binomial theorem. Examples. Grinstead and Snell: Sections 3.1 and 3.2 Lectures 1-3 slides (PDF)
Friday, June 25 Generalized combinations. Binomial theorem. Multinomial theorem. More combinatorial identities. Examples. Grinstead and Snell: Sections 3.1 and 3.2 Lectures 1-3 slides (PDF)
Monday, June 28 Sets. Introduction to discrete probability. Sample space. Events. Axioms of probability. Probability by counting. Examples. Properties of probability function. Inclusion-exclusion formula. Grinstead and Snell: Sections 1.2 and 4.1 Lectures 4-5 slides (PDF)
Wednesday, June 30 Events. Axioms of probability. Probability by counting. Properties of probability function. Inclusion-exclusion formula. Examples. Grinstead and Snell: Section 4.1 Lectures 4-5 slides (PDF)
Friday, July 2 Conditional probability. Independent and dependent events. Bayes' formula. Tossing coins. Examples. Grinstead and Snell: Section 4.1 Lectures 6-8 slides (PDF)
Monday, July 5 No class.
Wednesday, July 7 Conditional probability. Independent and dependent events. Bayes' formula. Tossing coins. Examples. Grinstead and Snell: Section 4.1 Lectures 6-8 slides (PDF)
Friday, July 9 Introduction to random variables. Binomial random variables. Expectation of a random variable. Examples. Grinstead and Snell: Sections 5.1 and 6.1 Lectures 6-8 slides (PDF)
Monday, July 12 Poisson random variables. Poisson vs Binomial. Examples. Grinstead and Snell: Sections 5.1 and 6.1 Lectures 9-13 slides (PDF)
Wednesday, July 14< Geometric random variables. Examples with discrete random variables. Grinstead and Snell: Sections 5.1 and 6.1 Lectures 9-13 slides (PDF)
Friday, July 16 Variance and standard deviation of discrete random variables. Examples. Markov inequality. Chebyshev inequality. Grinstead and Snell: Section 6.2 and 8.1 Lectures 9-13 slides (PDF)
Monday, July 19 Variance and standard deviation of discrete random variables. Markov inequality. Chebyshev inequality. Examples. Review. Grinstead and Snell: Section 6.2 and 8.1 Lectures 9-13 slides (PDF)
Wednesday, July 21 Review of Sections 3.1, 3.2, 1.2, 4.1, 5.1, and 6.1 in Grinstead and Snell Lectures 9-13 slides (PDF)
Friday, July 23 Continuous random variables. Probability density function. Expectations of continuous random variables. Examples: uniform, exponential, and normal random variables. Grinstead and Snell: Sections 2.2 (page 61) and 5.2 Lectures 14-16 slides (PDF)
Monday, July 26 Continuous random variables. Probability density function. Examples: uniform, exponential, and normal random variables. Expectation and variance of continuous random variables. Grinstead and Snell: Sections 2.2 (page 61), 5.2 and 6.3 Lectures 14-16 slides (PDF)
Wednesday, July 26 No class.
Friday, July 30 Continuous random variables. Probability density function. Examples: uniform, exponential, and normal random variables. Expectation and variance of continuous random variables. Grinstead and Snell: Sections 2.2 (page 61), 5.2 and 6.3 Lectures 14-16 slides (PDF)
Monday, August 2 Independent random variables. Sums of independent random variables. Law of Large Numbers. Central Limit Theorem. Examples. Grinstead and Snell: Sections 7.1, 7.2, 8.1, 8.2, 9.1, and 9.2 Lectures 17-19 slides (PDF)
Wednesday, August 4 Independent random variables. Sums of independent random variables. Law of Large Numbers. Central Limit Theorem. Examples. Grinstead and Snell: Sections 7.1, 7.2, 8.1, 8.2, 9.1, and 9.2 Lectures 17-19 slides (PDF)
Friday, August 6 Central Limit Theorem. Examples. Moment generating functions. Grinstead and Snell: Sections 9.1, 9.2, and 10.1 Lectures 17-19 slides (PDF)
Monday, August 9 Moment generating functions. Grinstead and Snell: Sections 10.1 and 10.3 Lectures 20-21 slides (PDF)
Wednesday, August 11 Moment generating functions. Review. Grinstead and Snell: Sections 10.1 and 10.3 Lectures 20-21 slides (PDF)