MATH 463/563 Probability I (Fall 2020)



Instructor: Yevgeniy Kovchegov
e-mail: kovchegy @math. oregonstate.edu
Office Hours: TW 5-6 or by appointment, via Zoom



Meets: live via Zoom MWF 11:00 am - 11:50 am, or prerecorded.

Grading scheme: Homework 30%, Online quizzes 25%, Online tests 45%

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.

Prerequisites: MATH 311 or instructor's approval. A minimum grade of C- is required in MTH 311.

Syllabus:  PDF file

Homework:   The homework assignments will need to be submitted in PDF format via Canvas and before the respective deadline. Late homework will not be accepted.

Homework #1 (due Friday, October 2):  HW 1 (PDF)

Homework #2 (due Wednesday, October 14):  HW 2 (PDF)

Homework #3 (due Monday, November 2):  HW 3 (PDF)

Homework #4 (due Monday, November 16):  HW 4 (PDF)

Homework #5 (due Wednesday, December 2):  HW 5 (PDF)

Schedule:
Wednesday, September 23  Introduction. Counting: Multiplication rule. Permutations. Combinations.   Grinstead and Snell: Sections 3.1 and 3.2   Lectures 1-3 slides (PDF)
Friday, September 25  Combinations. Pascal's triangle. Generalized combinations. Binomial theorem. Examples.   Grinstead and Snell: Sections 3.1 and 3.2   Lectures 1-3 slides (PDF)
Monday, September 28  Generalized combinations. Multinomial theorem. More combinatorial identities. Examples.   Grinstead and Snell: Sections 3.1 and 3.2   Lectures 1-3 slides (PDF)
Wednesday, September 30  Sets. De Morgan's laws. Introduction to discrete probability. Sample space. Events. Axioms of probability. Probability by counting. Examples.   Grinstead and Snell: Section 1.2   Huber: Chapter 41   Lectures 4-7 slides (PDF)
Friday, October 2  Introduction to discrete probability. Sample space. Events. Axioms of probability. Probability by counting. Examples. Properties of probability function.   Grinstead and Snell: Sections 1.2 and 4.1   Huber: Chapters 1 and 2   Lectures 4-7 slides (PDF)
Monday, October 5  Probability by counting. Examples. Properties of probability function. Inclusion-exclusion formula.   Grinstead and Snell: Section 4.1   Huber: Chapters 1 and 2   Lectures 4-7 slides (PDF)
Wednesday, October 7  Properties of probability function. Inclusion-exclusion formula.   Grinstead and Snell: Section 4.1   Huber: Chapters 1 and 2   Lectures 4-7 slides (PDF)
Friday, October 9  Conditional probability. Independent and dependent events. Bayes' formula. Examples.   Grinstead and Snell: Section 4.1   Huber: Chapters 6 and 7   Lectures 8-10 slides (PDF)
Monday, October 12  Conditional probability is a probability. Independent events. Bernoulli trials and tossing coins. Introduction to random variables. Expectation of a random variable. Bernoulli random variable. Binomial random variable. Examples.   Grinstead and Snell: Sections 5.1 and 6.1   Huber: Chapter 3   Lectures 8-10 slides (PDF)
Wednesday, October 14  Introduction to random variables. Expectation of a random variable. Bernoulli random variable. Binomial random variable. Poisson random variable.   Grinstead and Snell: Sections 5.1 and 6.1   Huber: Sections 7.1, 10.1, and 11.1   Lectures 8-10 slides (PDF)
Friday, October 16  Introduction to random variables. Expectation of a random variable. Bernoulli random variable. Binomial random variable. Poisson random variable.   Grinstead and Snell: Sections 5.1 and 6.1   Huber: Sections 7.1, 10.1, and 11.1   Lectures 11-16 slides (PDF)
Monday, October 19  Poisson random variable. Geometric random variables. Examples with discrete random variables. Variance and standard deviation.   Grinstead and Snell: Sections 5.1 and 6.2   Huber: Sections 7.1, 10.1, and 11.1   Lectures 11-16 slides (PDF)
Wednesday, October 21  Expectation of a function of a random variable. Variance and standard deviation of discrete random variables. Examples.   Grinstead and Snell: Section 6.2   Huber: Sections 7.1, 10.1, and 11.1   Lectures 11-16 slides (PDF)
Friday, October 23  Variance and standard deviation. Examples.   Grinstead and Snell: Section 6.2   Huber: Sections 7.1, 10.1, and 11.1   Lectures 11-16 slides (PDF)
Monday, October 26  Variance and standard deviation of discrete random variables. Markov inequality. Chebyshev inequality.   Grinstead and Snell: Sections 6.2 and 8.1   Huber: Chapters 11 and 25 Lectures 11-16 slides (PDF)
Wednesday, October 28  Markov inequality. Chebyshev inequality.   Grinstead and Snell: Sections 6.2 and 8.1   Huber: Chapters 11 and 25 Lectures 11-16 slides (PDF)
Friday, October 30  Review. Examples.   Grinstead and Snell: Sections 3.1, 3.2, 1.2, 4.1, 5.1, and 6.1   Lecture 17 slides (PDF)
Monday, November 2  Continuous random variables. Probability density function. Examples: uniform and exponential random variables.   Grinstead and Snell: Sections 2.2, 6.3, and 8.1   Huber: Chapters 4 and 8   Lectures 18-22 slides (PDF)
Wednesday, November 4  Continuous random variables. Probability density function. Normal random variables. Expectations of continuous random variables.   Grinstead and Snell: Sections 2.2 and 6.3   Huber: Chapters 4 and 8   Lectures 18-22 slides (PDF)
Friday, November 6  Normal random variables. Expectation and variance of continuous random variables. Examples.   Grinstead and Snell: Sections 2.2 (page 61), 5.2 and 6.3   Huber: Chapters 8 and 18   Lectures 18-22 slides (PDF)
Monday, November 9  Expectation and variance of continuous random variables. Distribution of a function of a random variable. Examples.   Grinstead and Snell: Sections 2.2 (page 61), 5.2 and 6.3   Huber: Chapters 8 and 18   Lectures 18-22 slides (PDF)
Friday, November 13  Expectation and variance of continuous random variables. Distribution of a function of a random variable. Examples.   Grinstead and Snell: Sections 2.2 (page 61), 5.2 and 6.3   Huber: Chapters 8 and 18   Lectures 18-22 slides (PDF)
Monday, November 16  Independent random variables. Sums of independent random variables.   Grinstead and Snell: Sections 7.1 and 7.2   Lectures 23-28 slides (PDF)
Wednesday, November 18 No class.
Friday, November 20  Sums of independent random variables. Examples.   Grinstead and Snell: Sections 7.1 and 7.2   Lectures 23-28 slides (PDF)
Monday, November 23  Sums of independent random variables. Examples.  Grinstead and Snell: Sections 7.1 and 7.2   Lectures 23-28 slides (PDF)
Wednesday, November 25  Law of Large Numbers. Central Limit Theorem.   Grinstead and Snell: Sections 7.1, 7.2, 9.1, and 9.2   Lectures 23-28 slides (PDF)
Monday, November 30  Central Limit Theorem. De Moivre-Laplace Theorem. Stirling's formula. Examples.   Grinstead and Snell: Sections 9.1, and 9.2   Lectures 23-28 slides (PDF)
Wednesday, December 2  Central Limit Theorem. De Moivre-Laplace Theorem and its proof. Stirling's formula.   Grinstead and Snell: Sections 9.1, and 9.2   Lectures 23-28 slides (PDF)
Friday, December 4  Examples. Review.   Lecture 29 slides (PDF)