Math 3160 Probability Spring 2022

Section 002

Sasha Teplyaev

Math 3160 — Probability (Syllabus Spring 2022)

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 18):

HW 2 (January 20):

HW 3 (January 25, 27):

HW 4 (February 1):

HW 5 (February 3):

HW – (February 8):

  • Review of chapters 1, 2, 3, 4, 5, 6.

HW – (February 10):

  • In-class Test on Chapters 1, 2, 3, 4, 5, 6. You can bring one two-sided hand-written page of notes with formulas.

HW 7 (February 15):

HW 8-9 (February 18, 22):

HW 10 (February 25):

 

HW 11 (March 1):

HW 12 (March 3):

 

HW – (March 8):

  • Review of chapters 7, 8, 9, 10, 11, 12.

HW – (March 10):

  • In-class Test on Chapters 7, 8, 9, 10, 11, 12. You can bring one two-sided hand-written page of notes with formulas.

HW – (March 22, 24):

  • Chapters 11, 12.

HW – (March 29, 7):

HW – (April 5, 24):

HW – (April 12, 14):

  • Thursday April 14: in-class Test on Chapters 11, 12, 13, 14. You can bring one two-sided hand-written page of notes with formulas.

HW – (April 19, 21):

HW – (April 26, 28):

  • review/extra chapters

 

Final Exam:
Monday
05/02/2022
03:30pm–05:30pm
KNS201

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UNDER CONSTRUCTION

(all future dates are tentative) –>