Tag Archives: law of large numbers

Truncation Lemma Statement: Let $X_n$ be a sequence of IID variables with finite mean, and let $Y_n$ = $X_n I_{|X_n| \leq n}$. Then $\sum \frac{Var(Y_n)}{n^2} < \infty$. Proof: Lemma: If $c \geq 0$, then $c^2 \sum_{n=1}^\infty \frac{I_{|c| \leq n}}{n^2} \leq 1 … Continue reading →