0
$\begingroup$

Can someone please give me an example for sequence $\{X_n\} $ of independent random variables, such that $$ E[|X_n|]<5 $$ for each n, and such that the weak law of large numbers doesn't hold for it ?

$\endgroup$
3
$\begingroup$

Nothing probabilistic here... Try $X_n=1$ with full probability if $4^k\leqslant n\lt2\cdot4^k$ for some integer $k$, and $X_n=0$ with full probability otherwise.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.