Math 3160 Probability — Fall 2022

Sasha Teplyaev

Math 3160 — Probability (Syllabus Fall 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 (August 29):

HW 2 (September 1):

HW 3 (September 6,8):

HW 5 (September 13, Tuesday):

HW 6 (September 15, Thursday):

 

HW 7 (September 20, Tuesday):

     

    HW – (September 27, Tuesday):

    • Review of chapters 1, 2, 3, 4, 5, 6, 7.

     

    HW– (September 29, Thursday):

    • In-class Test on Chapters 1, 2, 3, 4, 5, 6, 7. You can bring one two-sided hand-written page of notes with formulas.

     

    HW 8-9 (Otoberber 4, Tuesday)

    HW 10 (October 6, Thursday):

    HW 11 (October 11, 13):

    HW 12 (October 18, 20):

    HW – (October 25):

    • Review of chapters 6, 7, 8, 9, 10, 11, 12.

    HW – (October 27):

    • In-class Test on Chapters 6, 7, 8, 9, 10, 11, 12. You can bring two two-sided hand-written pages of notes with formulas.

      HW – (November 1,3):

      HW 14 (November 8,9):

       

      HW – (November 15, Tuesday):

      • Review of chapters 11, 12, 13, 14.

      HW – (November 17):

      • Thursday, November 17: in-class Test on Chapters 11, 12, 13, 14. You can bring three two-sided hand-written pages of notes with formulas.

      Table of distributions.
      Discrete: Binomial, Poisson, Geometric
      Continuous: Normal, Uniform, Exponential

      HW – (November 29, December 1):

      HW – (December 6,8):

      • review/extra chapters

       

      Final Exam: tba

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      UNDER CONSTRUCTION

      (all future dates are tentative) –>