Topics

Counting principles, permutations, combinations, and the foundations of discrete probability.

No prerequisites

Definition, PMF, PDF, CDF, expectation, variance, and standard transformations.

Conditional probability, Bayes' theorem, law of total probability, and independence.

Bernoulli, Binomial, Geometric, Poisson — their properties and common applications.

Uniform, Exponential, Normal, Gamma — densities, moments, and key identities.

Joint, marginal, and conditional distributions; covariance, correlation, and independence of random vectors.

Monte Carlo integration, variance reduction, importance sampling, and random number generation.

Discrete-time Markov chains, transition matrices, stationary distributions, and hitting times.

Estimators, MLE, confidence intervals, hypothesis testing, asymptotic theory, stationarity, ARMA models, and forecasting.