Strong Law of Large Numbers

askazy

New Member
#1
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
#2
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.

The answer to your question is essentially right there.
 

askazy

New Member
#3
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.

The answer to your question is essentially right there.
Thank you, solved.