Strong Law of Large Numbers

New Member
If $$X_n$$ is a sequence of random variables and $$Cov(X_i,X_j)=0$$ for all i,j and $$Var(X_j)\leq c$$ for all j. Show that $$X_n$$ satisfies the strong law of large numbers.

I don't have idea of how to make it, because almost surely convergence is hard to proof.

Dragan

Super Moderator
Well, it's not so difficult. Take some time and look at the following reference book;

Polansky, Alan. (2011). Introduction to Statistical Limit Theory. Section 3.6 pp. 124-131.