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 Dec 29 awarded Popular Question Dec 19 awarded Notable Question Aug 3 awarded Popular Question Nov 23 awarded Supporter Nov 23 accepted Sample variance converge almost surely Nov 23 comment Sample variance converge almost surely That makes sense. Thank you! Nov 23 comment Sample variance converge almost surely But the $\mu$ can be infinity, I think you cannot apply strong law of large numbers. And you haven't used the condition that the variance is finite. Nov 23 asked Sample variance converge almost surely Oct 26 asked Is my proof rigorous/complete? Oct 16 suggested rejected edit on Bounded random variable Oct 16 comment Bounded random variable That's correct. I misunderstood the question. I thought I should find a Y for all all ε>0, P(X≠Y)<ε. Oct 16 awarded Scholar Oct 16 accepted Bounded random variable Oct 13 comment Bounded random variable It's obviously Y can cover $X\,1_{\left|X\right|\leq x}$ for arbitrary x. But how do you deal with the part $X\,1_{\left|X\right|>x}$? How can it be less than any positive number when you fix a x? Thanks! Oct 13 comment Bounded random variable What about the part {X>x}. Could you explain a little bit more? Oct 13 awarded Editor Oct 13 revised Bounded random variable added 1 characters in body Oct 12 awarded Student Oct 12 asked Bounded random variable