Markov Chains & Simulation Foundations – Practice Quiz

Finite Markov chains and simulation foundations: interpret transition matrices, calculate multi-step probabilities and stationary distributions, and check irreducibility, aperiodicity and detailed balance. Distinguish stationarity from convergence and independent sampling, simulate transitions with uniform random numbers and analyze counterexamples to common long-run claims. Includes original single-select and multiselect scenarios, worked reasoning and explanations of each distractor. Prerequisites: conjugate models, probability vectors and basic matrix multiplication. Authored from the saved Statistics & Probability syllabus; intended for progressive independent practice.

Further reading: Harvard Stat 110: Markov chains.