Convergence, Inequalities & Limit Theorem Proofs – Practice Quiz

Build a rigorous understanding of convergence, inequalities & limit theorem proofs through 20 original single-select and multiselect questions. Begin with core definitions, then work through calculations, assumptions, counterexamples and advanced diagnostic challenges.

Prerequisites: the earlier core Statistics curriculum, including probability distributions, expectation, calculus and the preceding mathematical-statistics sets.

Competencies: Define modes of stochastic convergence; Apply Markov, Chebyshev and Jensen inequalities; Prove a finite-variance weak law and derive bounds; Construct rare-event counterexamples for moment convergence; Distinguish marginal weak convergence and pathwise closeness; Develop a characteristic-function CLT proof sketch; State finite-moment and MGF assumptions precisely; Use almost sure convergence criteria and distinguish proof sufficiency. Every item includes a worked explanation and reasons for rejecting distractors.

Further reading: Convergence, inequalities, laws of large numbers and CLT, Lindeberg–Levy iid CLT and finite variance, Definition and implications.