This Probability Theory course (Statistics 110) provides a deep and structured introduction to probability and its applications in statistics. It begins with foundational concepts such as probability rules, counting methods, and axioms of probability, helping learners understand how probability systems are built.
The course explores important real-world problems like the Birthday Problem and introduces key ideas such as properties of probability and conditional probability. Students will also learn advanced concepts including the Law of Total Probability, Monty Hall Problem, and Simpson’s Paradox, which demonstrate how probability can behave in counterintuitive ways.
The second part of the course focuses on random variables and probability distributions. Learners will study expectation, indicator random variables, and the linearity of expectation, which are essential tools in statistical reasoning. The course also introduces classic probability models such as the Poisson distribution.
Throughout the lectures, complex ideas are explained using clear examples, logical reasoning, and step-by-step proofs, making the course suitable for students, researchers, and anyone interested in mathematics, data science, or quantitative analysis.
By the end of this course, learners will have a strong foundation in probability theory and be able to analyze random processes, interpret distributions, and apply probabilistic thinking in real-world problems.
