State the Law of Large Numbers.
easyAnswer
- As the sample size grows, the sample mean converges to the true expected value.
- Weak LLN: convergence in probability.
- Strong LLN: convergence almost surely.
- This justifies estimating expectations by averaging samples — the foundation of Monte Carlo estimation.
Check yourself — multiple choice
- Sample mean diverges as n grows
- Sample mean converges to the true expectation as n grows
- LLN applies only to normal distributions
- LLN implies the CLT rate
LLN: averages converge to expected values.
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Practise Statistics Fundamentals
215 interview questions in this topic.