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Mathematics

Probability

Study probability through mathematical proofs, intuitive explanations, real-life applications, and datasets.

Instructor Dr. Waleed A. Yousef Adjunct Professor, University of Victoria, Canada
A Galton board showing random trials forming a bell-shaped distribution

01

Course overview

Study probability through mathematical proofs, intuitive explanations, real-life applications, and datasets.

02

What you will learn

This standard course in probability theory is designed for students in applied sciences. It covers the fundamental principles of probability theory and emphasizes the importance of both mathematical rigor and intuition. To achieve this objective, the course includes comprehensive coverage of proofs, intuitive explanations of mathematical concepts, and numerous examples showcasing real-life applications and real datasets.

By the end of the course, students will gain a solid understanding of basic probability concepts, providing them with comfort and proficiency when encountering such concepts in their future studies in computer science.

The course will extensively cover the first six chapters of the book, including topics such as counting, the law of total probability, Bayes' rule, random variables, discrete and continuous random variables, moments, multivariate distributions, joint density functions, marginal distributions, covariance, functions of random variables, transformations, and the Central Limit Theorem.

03

Lecture syllabus

Video titles and durations as published on Arabsera. The advertised lecture total may differ from the number of video entries, which can include introductions, tutorials, and split sessions.

Video titles and durations 26
  1. 01 (Sec. 1.1 - 1.4) Introduction, Sample Space, Probability Measure and Counting Methods
  2. 02 (Sec. 1.4) Counting Methods
  3. 03 (Sec. 1.5) Conditional Probability
  4. 04 (Sec. 1.5 - 1.6) Conditional Probability and Independence
  5. 05 (Sec. 2.1) Discrete Random Variable
  6. 06 (Sec. 2.1) Discrete Random Variable
  7. 07 (Sec. 2.2) Continuous Random Variable
  8. 08 (Sec. 2.2) Continuous Random Variable
  9. 09 (Sec. 2.3) Functions of Random Variables
  10. 10 (Sec. 2.3) Functions of Random Variables
  11. 11 (Sec. 3.1 - 3.2) Introduction and Discrete Random Vectors
  12. 12 (Sec. 3.3) Continuous Random Vectors
  13. 13 (Sec. 3.4) Independent Random Vectors
  14. 14 (Sec. 3.5) Conditional Distributions
  15. 15 (Sec. 3.6.1) Single Function of Jointly Distributed Random Variables
  16. 16 (Sec. 3.6.2) p Functions of p Random Variables ( Space Transformation )
  17. 17 (Sec. 3.7) Extrema and Order Statistics
  18. 18 (Sec. 4.1) The Expected Value of a Random Variable
  19. 19 (Sec. 4.1.1 - 4.1.2) Expectations of Functions and Linear Combinations of Random Variable
  20. 20 (Sec. 4.2) Variance and Standard Deviation
  21. 21 (Sec. 4.3) Covariance and Correlation
  22. 22 (Sec. 4.3) Covariance and Correlation
  23. 23 (Sec. 4.4) Conditional Expectation and Prediction
  24. 24 (Sec. 4.5 - 4.6) The Moment-Generating Function and Approximate Methods
  25. 25 (Sec. 5.1 - 5.2) The Law of Large Numbers, Convergence in Distribution and CLT
  26. 26 Appendix A - Computer Simulation

04

Teaching support (check your plan)

  • Discussion groups
  • TA-human texting for Q&A
  • TA-GPT (coming soon)

05

Textbook

Rice, J.A., “Mathematical statistics and data analysis”. 3rd ed.

06

Certificate

Awarded after passing a brief sample exam, which you may attempt multiple times.