In this lecture, the professor discussed classical inference, simple binary hypothesis testing, and composite hypotheses testing.

1. Probability Models and Axioms
2. Conditioning and Bayes' Rule
3. Independence
4. Counting
5. Discrete Random Variables I
6. Discrete Random Variables II
7. Discrete Random Variables III
8. Continuous Random Variables
9. Multiple Continuous Random Variables
10. Continuous Bayes' Rule; Derived Distributions
11. Derived Distributions (ctd.); Covariance
12. Iterated Expectations
13. Bernoulli Process
14. Poisson Process I
15. Poisson Process II
16. Markov Chains I
17. Markov Chains II
18. Markov Chains III
19. Weak Law of Large Numbers
20. Central Limit Theorem
21. Bayesian Statistical Inference I
22. Bayesian Statistical Inference II
23. Classical Statistical Inference I
24. Classical Inference II
25. Classical Inference III

An subject on the modeling and analysis of random phenomena and processes, including the basics of statistical inference. Nowadays, there is broad consensus that the ability to think probabilistically is a fundamental component of scientific literacy.

The aim of this class is to introduce the relevant models, skills, and tools, by combining mathematics with conceptual understanding and intuition.

This course is suitable to both undergraduate and graduate students.