Statistics I (Probability and Distributions)

Statistics I covers the essential building blocks of probability theory and statistical distributions. You will learn how to describe random events, calculate probabilities using formal rules, and apply counting techniques for complex problems. The course explores both discrete and continuous random variables, major probability distributions, and key concepts like expectation, variance, and moment-generating functions. It concludes with the foundational limit theorems that underpin much of modern statistical inference.

What you’ll learn

Define and work with experiments, sample spaces, events, and axioms of probability.
Apply addition and multiplication rules, conditional probability, and Bayes’ theorem.
Use permutations, combinations, and multinomial coefficients in probability problems.
Differentiate between discrete and continuous random variables and understand PMFs and PDFs.
Analyze key discrete distributions (uniform, binomial, geometric, Poisson).
Analyze key continuous distributions (uniform, normal, exponential, gamma).
Compute expectation, variance, and apply moment-generating functions.
Understand and apply the Law of Large Numbers and the Central Limit Theorem.