apologies for what might be a dumb question. I'm studying the law of large numbers, and I'm stuck on the following math
Why do we need to make it $\frac{1}{n^2}$when pulling it out of the summation?
Any help would be greatly appreciated! Thanks in advance.
Because for all $a\in\mathbb R$ and random variable $X$, $\operatorname{var}(aX)=a^2\operatorname{var}(X)$, which is straightforward from the definition of $\operatorname{var}$.