# MATH 361 - Introduction to Probability

## Summer 2017

 Instructor: Yevgeniy Kovchegov e-mail: kovchegy @math. oregonstate.edu Office: Kidder 368C Office Phone No: 7-1379 Office Hours: M, W 2:30-4:00
 Homeworks and Quizzes 30% Midterm 30% Final 40%
Place and time: MW 4:00pm to 6:00pm, room GILK 104.

Textbook: 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/amsbook.mac.pdf
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 instructor's approval.

Syllabus:  .doc

Quizzes and Homework: There will be five homework assignments, and frequent quizzes given in class.

Homework #1 (due Wednesday, June 29):  HW 1 (PDF)

Homework #2 (due Wednesday, July 12):  HW 2 (PDF)

Homework #3 (due Wednesday, July 19 Monday, July 24):  HW 3 (PDF)

Homework #4 (due Wednesday, August 2 Monday, August 7):  HW 4 (PDF)

Midterms: There will be a midterm exam on Wednesday, July 26.
The midterm will cover the material presented in the first five weeks of lectures and is going to be given in class. The exam is closed books. However a 8.5 by 11 inch sheet with HANDWRITTEN notes on both sides is allowed. No scientific calculators and other devices with built in probability tools will be allowed.

Here are the topics that will be covered on the midterm: Sample space; Events; Probability; Inclusion-exclusion formula; Conditional probability; Bayes' formula; Independent events; Dependent events; Permutations; Binomial coefficients; Binomial distribution; Binomial theorem; Discrete random variables; Expectation.

Final Exam:   Wednesday, August 16   Location: GILK 104
The exam is closed books. However a 8.5 by 11 inch sheet with HANDWRITTEN notes on both sides is allowed. No scientific calculators and other devices with built in probability tools will be allowed.

Schedule:
Monday, June 26  Introduction. Counting: Multiplication rule. Permutations. Combinations. Generalized combinations. Pascal's triangle. Examples. Sections 3.1 and 3.2 Lecture 1 slides (PDF)
Wednesday, June 28  Generalized combinations. Binomial theorem. Multinomial theorem. More combinatorial identities. Examples. Sections 3.1 and 3.2 Lecture 2 slides (PDF)
Monday, July 3  No class.
Wednesday, July 5  Sets. Introduction to discrete probability. Sample space. Events. Axioms of probability. Probability by counting. Examples. Properties of probability function. Inclusion-exclusion formula. Sections 1.2 and 4.1 Lecture 3 slides (PDF)
Monday, July 10  Properties of probability function. Inclusion-exclusion formula. Conditional probability. Independent and dependent events. Bayes' formula. Examples. Section 4.1 Lecture 4 slides (PDF)
Wednesday, July 12  Independent and dependent events. Bayes' formula. Tossing coins. Introduction to random variables. Binomial random variable. Expectation of a random variable. Examples. Sections 4.1, 5.1 and 6.1 Lecture 5 slides (PDF)
Monday, July 17  Poisson random variables. Poisson vs Binomial. Geometric random variables. Examples with discrete random variables. Variance and standard deviation. Sections 5.1 and 6.2 Lecture 6 slides (PDF)
Wednesday, July 19  Variance and standard deviation of discrete random variables. Examples. Markov inequality. Chebyshev inequality. Sections 6.2 and 8.1 Lecture 7 slides (PDF)
Friday, July 21  Extended office hours (in GILK 104)
Monday, July 24  Review. Examples. The review of Sections 3.1, 3.2, 1.2, 4.1, 5.1, and 6.1 Lecture 8 slides (PDF)
Wednesday, July 26  Midterm
Monday, July 31  Continuous random variables. Probability density function. Expectations of continuous random variables. Examples: uniform and exponential random variables. Sections 2.2 and 6.3 Lecture 9 slides (PDF)