← STAT 02360 · Probability and Random Variables
STAT 02360 · Named distributions & limit ideas
Law of large numbers / CLT intuition
Definition
LLN: sample averages X̄ converge to μ as n→∞ (in probability). CLT: for large n, X̄ is approximately Normal(μ, σ²/n) even if the population is not normal.
Read this
CLT explains why z-procedures and many “bell-shaped sampling” heuristics work.
Standard error of the mean shrinks like 1/√n.
LLN is about centering on μ; CLT is about the shape of fluctuations around μ.
Drill with flashcards
Flip through these until you can say the answer before revealing it.
Flashcards · 1 / 3
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Try this
Attempt each problem first, then open the worked solution.
1.Explain why polling more people shrinks the margin of error like 1/√n.