Exercise · ZW-LAW-OF-LARGE-NUMBERS-007 · ★★☆ Intermediate
With \(\sigma^2=9\) and \(n=1000\), what bound does Chebyshev give for \(P(|\bar X_n-\mu|\ge0.3)\)?
Choose one option.
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- A. \(0.1\)
Explanation
\(\dfrac{\sigma^2/n}{\varepsilon^2}=\dfrac{9/1000}{0.09}=0.1\).
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.
\[\bar X_n=\dfrac1n\sum_{i=1}^{n}X_i\ \xrightarrow[n\to\infty]{}\ \mu\]
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