From a sample to a conclusion.
Nine units. Probability first, then inference — the discipline of reasoning under uncertainty.
Descriptive statistics
Mean, median, mode, variance, standard deviation, the shape of a distribution.
Unit 2 · Sample spaceProbability basics
Sample spaces, events, axioms, conditional probability, independence, Bayes' rule.
Unit 3 · DistributionsRandom variables
Discrete and continuous, PMF, PDF, CDF, expectation, variance of a variable.
Unit 4 · The usual suspectsNamed distributions
Binomial, Poisson, geometric, normal, exponential — when each one applies.
Unit 5 · MultipleJoint distributions
Joint, marginal, conditional distributions, covariance, correlation.
Unit 6 · TheoremsLimit theorems
Law of large numbers, central limit theorem, what "large n" actually buys you.
Unit 7 · EstimationEstimators & sampling
Bias, variance, consistency, MLE, confidence intervals for means and proportions.
Unit 8 · TestsHypothesis testing
Null and alternative, p-values, Type I/II errors, z-test, t-test, chi-square.
Unit 9 · Real dataRegression & correlation
Linear regression, least squares, residuals, multiple regression, model pitfalls.