# math 3160 Spring 2020 –

Section 007

Sasha Teplyaev

Math 3160 — Probability (Revised Syllabus Spring 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)

Current sections of Math 3160

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 (January 20 — January 24):

HW 2 (January 27 — January 31):

HW 3 (February 3 — February 7):

HW 4 (February 10 — February 14):

HW 5 (February 17 — February 21):

HW 6 (February 24 — February 28):

HW 7 (March 2 — March 6):

HW 8 (March 9 — March 13):

* Spring Break *

HW 9 (March 23 — March 27)

HW 10 (March 30 — April 3)

HW 11 (April 6 — April 10)

HW 12 (April 13 — April 17)

HW 13 (April 20 — April 24)

HW 14 (April 27 — May 1)

Final Exam:

• take-home open-book Final Exam Sunday May 3, 9am — Saturday May 9, 9pm.

Former Final Exam Schedule: 5/8/2020, Friday 3:30pm–5:30pm MONT 321

(all future dates are tentative)