Central Limit Theorem

In WLLN we took the average over iid RV’s. For the CLM these RVs need to be special: they need to have mean zero.

Now we will not take the conventional average $\frac{1}{n}\sum X_i$. We will take this average $\frac{1}{\sqrt{n}}\sum X_i$. Why is this special? well the variance of this is independent of $n$. Which is interesting.