Commit aaae7145 authored by Vincent Tam's avatar Vincent Tam

Post WLLN Ex: fixed math in direct quote

parent 3ebc403d
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......@@ -23,9 +23,9 @@ unsure how to do so.
https://math.stackexchange.com/q/3021650/290189, I'll assume the independence of
$(X_n)$. By Chebylshev's inequality,
> $$P(|\bar{X}_n|>\epsilon) = P(|\sum_{k=1}^n X_k|> n\epsilon) \le
> <div>$$P(|\bar{X}_n|>\epsilon) = P(|\sum_{k=1}^n X_k|> n\epsilon) \le
\frac{\sum_{k=1}^n var(X_k)}{n^2 \epsilon^2} = \frac{\sum_{k=1}^n
(\ln(k))^2}{n^2 \epsilon^2} \le \frac{(\ln(n))^2}{n \epsilon} \to 0$$
(\ln(k))^2}{n^2 \epsilon^2} \le \frac{(\ln(n))^2}{n \epsilon} \to 0$$</div>
Recall: $(\ln(n))^p/n \to 0$ whenever $p \ge 1$. To see this, make a change of
variables $n = e^x$, so that it becomes $x^p / e^x$.
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