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 May12 asked If the sum of two independent random variables is in $L^2$, is it true that both of them are in $L^1$? May7 comment hat problem and probability If the colors are assigned at equal probability and independently, you will not be able do better than 1/2. May5 revised Simple probability problem? typos May4 answered Simple probability problem? Mar10 awarded Popular Question Mar2 awarded Notable Question Dec8 awarded Popular Question Nov17 comment The limit of integer valued random variables must be integer valued? OK. BTW, does my example shows that the portmanteau theorem works only for random variables on $\mathbb R$? Nov17 accepted The limit of integer valued random variables must be integer valued? Nov17 comment The limit of integer valued random variables must be integer valued? It's not clear whether the author meant to define $D_n$ and $D$ in $\mathbb R$ or compactification of $\mathbb R$. That's a question that comes to me again and again -- When the author says "random variables", does he/she allow them to take $\infty$ as value or not? Nov17 comment The limit of integer valued random variables must be integer valued? Thanks. I'm actually aware of this theorem and it is how I thought I had proved it. But when I came up with the "counter example" that I got confused again. Can we say that $\infty \in \mathbb Z$? Nov17 asked The limit of integer valued random variables must be integer valued? Nov6 awarded Popular Question Oct24 awarded Popular Question Sep1 awarded Yearling Aug31 comment Martingale with bounded increment. @Did, I will remember to do that next time! Aug30 accepted Martingale with bounded increment. Aug30 asked Martingale with bounded increment. Aug1 revised Sum of positive i.i.d. random variables. added 8 characters in body Jul19 accepted The extinction probability of Galton-Watson process from a martingale perspective.