Stats 2 Book: Probability & Statistics
Stats 2 Book: Probability & Statistics
Welcome to the digital textbook for Statistics 2. This course covers a comprehensive range of topics in probability and statistics, organized sequentially from basic concepts and discrete probability to continuous distributions, statistical inference, and regression.
Course Content
Chapters
All chapters for Stats 2 Book
Basic Concepts
Foundational mathematical framework for probability, including definitions, axioms, conditional probability, and Bayes' Theorem.
Sampling and Repeated Trials
Models based on repeated independent trials, focusing on Bernoulli trials and sampling methods.
Discrete Random Variables
Formalizing random variables, probability mass functions, and independence.
Summarizing Discrete RVs
Expected value, variance, standard deviation, and correlation for discrete distributions.
Continuous Probabilities
Probability models for uncountable sample spaces, densities, and continuous distributions.
Summarising Continuous RVs
Expectation, variance, moments, and moment generating functions for continuous variables.
Sampling and Descriptive Statistics
The transition from probability to statistics: empirical distributions and sample estimates.
Limit Theorems
Law of Large Numbers, Central Limit Theorem, and sampling distributions.
Estimation & Hypothesis Testing
Methods for inferring unknown parameters and testing conjectures.
Linear Regression
Modeling linear relationships, least squares, and regression inference.