Question and Theorem as in the Pictures.

Theorem 9.9. (Law of large numbers with finite variance) Suppose that we have i.i.d. random variables X1, X2, X3, ... with finite mean E[X1] = u and finite variance Var(X]) = 02. Let Sn = X1+ ... + Xn. Then for any fixed & > 0 we have lim P Sn - M 2 and that there is a constant c > 0 so that | Cov(Xi, Xit1)| 0 we have lim P Sn - U