# math 3160 Fall 2020

Section 001

Sasha Teplyaev

Math 3160 — Probability (Syllabus Fall 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 (August 31 — September 4):

HW 2 (September 7 — September 11):

HW 3 (September 14 — September 18):

HW 4 (September 21 — September 25):

HW 5 (September 28 — October 2):

HW 6 (October 5 — October 9):

HW 7 (October 12 — October 15):

HW 8 (October 19 — October 23):

HW 9 (October 26 — October 30)

HW 10 (November 2 — November 6)

HW 11 (November 9 — November 13)

HW 12 (November 16 — November 20)

## Take home test  December 3–6 (Thursday — Sunday)

Final Exam:

• ### take-home open-book Final Exam: from Thursday December 17 to Sunday December 20

• office hour time for the final exam:
 12/18/2020, Friday 8:00AM – 10:00AM

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(all future dates are tentative) –>