Math 4800/5080, Probability Theory - FALL 2024

Instructor: Vahan Huroyan

Email: vahan (dot) huroyan (at) slu (dot) edu

Section Time: MWF 15:10 - 16:00

Section Room: Ritter Hall, 323

Office Hours: Ritter Hall 113:

Course Syllabus: [here]

Textbook: Introduction to Probability, Second Eddition, by Jessica Hwang and Joseph K. Blitzstein.

Extra Reading: Introduction to Probability, by David F. Anderson, Benedek Valkó, Timo Seppäläinen.


Announcements:

  • Lecture 1, Aug. 21: Sample spaces, set theory overview (Section 1.2)
  • Lecture 2, Aug. 23: Counting (Section 1.3)
  • Lecture 3, Aug. 26: Counting (Section 1.4)
  • Lecture 4, Aug. 28: Probability spaces, probability function (Sections 1.6)
  • Lecture 5, Aug. 30: Properties of probability, inclusion-exclusion theorem (Section 1.6)
  • Lecture 6, Sep. 4: Conditional probability (Section 2.2)
  • Lecture 7, Sep. 6: Conditional probability, examples (Section 2.2)
  • Lecture 8, Sep. 9: Bayes' rule, the law of total probability (Sections 2.3, 2.5)
  • Lecture 9, Sep. 11: Independence of events (Section 2.5)
  • Lecture 10, Sep. 13: Examples, conditional independence (Section 2.5)
  • Lecture 11, Sep. 16: Independence of a collection of events, examples (Section 2.7)
  • Lecture 12, Sep. 18: Random Variables (Section 3.1)
  • Lecture 13, Sep. 20: Bernoulli, Binomial, Geometric, and Hypergeometric (Sections 3.3, 3.4)
  • Lecture 14, Sep. 23: Cumulative distribution function (CDF) (Section 3.6)
  • Lecture 15, Sep. 27: Functions of random variables (Section 3.7)
  • Lecture 16, Sep. 30: Review
  • Lecture 17, Oct. 2: Midterm 1
  • Lecture 18, Oct. 4: Independence of random variables (Section 3.8)
  • Lecture 19, Oct. 7: Connections between Binomials and Hypergeometric (Section 3.9)
  • Lecture 20, Oct. 9: Expectation (Sections 4.1, 4.2, 4.5)
  • Lecture 21, Oct. 11: Geometric and Negative Binomial (Section 4.3)
  • Lecture 22, Oct. 14: Variance (Section 4.6)
  • Lecture 23, Oct. 16: Poisson random variable (Section 4.7)
  • Lecture 24, Oct. 18: Connections between Poisson and Binomial (Section 4.8)
  • Lecture 25, Oct. 21: Continuous Random Variables; PDF; Uniform distribution (Sections 5.1, 5.2)
  • Lecture 26, Oct. 23: Normal distribution (Section 5.3)
  • Lecture 27, Oct. 28: Exponential distribution, Poisson processes (Sections 5.4, 5.5)
  • Lecture 28, Oct. 30: Moments, Summaries of distributions (Section 6.1)
  • Lecture 29, Nov. 1: Interpreting Moments, Sample Moments (Sections 6.2, 6.3)
  • Lecture 30, Nov. 4: Moment generating function (Section 6.4)
  • Lecture 31, Nov. 6: Sums of independent r.v.s via MGFs (Section 6.6)
  • Lecture 32, Nov. 8: Joint, Marginal and conditional Distributions | Discrete (Section 7.1)
  • Lecture 33, Nov. 11: Joint, Marginal and conditional Distributions | Continuous (Sections 7.1, 7.2)
  • Lecture 34, Nov. 13: Review
  • Lecture 35, Nov. 15: Midterm 2
  • Lecture 36, Nov. 18: Covariance and Correlation (Section 7.3)
  • Lecture 37, Nov. 20: Multinomial Distribution (Section 7.4)
  • Lecture 38, Nov. 22: Multivariate Normal (Section 7.5)
  • Lecture 39, Nov. 25: Cauchy-Schwarz Inequality, Jensen's Inequality (Sections 10.1.1, 10.1.2)
  • Lecture 40, Dec. 2: Markov, Chebyshev, Chernoff: bounds on tail probabilities (Section 10.1.3)
  • Lecture 41, Dec. 4: Law of large numbers (Section 10.2)
  • Lecture 42, Dec. 6: Central Limit Theorem (Section 10.3)

  • Homework:

  • HW 1: posted 09/02, due 09/13
  • HW 2: posted 09/14, due 09/26
  • HW 3: posted 09/27, due 10/16
  • HW 4: posted 10/17, due 10/31
  • HW 5: posted 11/01, due 11/13
  • HW 6: posted 11/14, due 12/06