Compare LLN and CLT with heavy tails

Q: Compare LLN and CLT with heavy tails

This is a Statistics & Math interview question from Other for Data Scientist roles. View the full question and solution on PracHub.

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Question

Explain the Law of Large Numbers vs the Central Limit Theorem, including their assumptions and convergence guarantees. Construct a concrete counterexample using a Pareto(α=1.5, xm=1) distribution: (a) Does the LLN hold for the sample mean? (b) Does the classical CLT hold for the standardized sample mean? (c) What limiting behavior do you expect for the properly scaled sum? Justify rigorously, and outline a simulation to empirically verify your claims.

Compare LLN and CLT with heavy tails

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