Exercise · ZW-LAW-OF-LARGE-NUMBERS-004 · ★★☆ Intermediate
With \(\sigma^2=4\), what is the smallest \(n\) such that \(\operatorname{Var}(\bar X_n)\le0.01\)?
Choose one option.
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- D. \(400\)
Explanation
We need \(4/n\le0.01\), that is, \(n\ge400\).
Review the concept: Law of large numbers
The law of large numbers states that the average \(\bar X_n\) of \(n\) independent observations of a variable \(X\) approaches its expectation \(\mu\) as \(n\) grows.
\[\bar X_n=\dfrac1n\sum_{i=1}^{n}X_i\ \xrightarrow[n\to\infty]{}\ \mu\]
More practice problems: law of large numbers
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