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May
13
revised If the sum of two independent random variables is in $L^2$, is it true that both of them are in $L^1$?
added 148 characters in body
May
13
comment If the sum of two independent random variables is in $L^2$, is it true that both of them are in $L^1$?
@Batman That's why proving $X$ and $Y$ are in $L^1$ should be an easier task, isn't it?
May
13
comment If the sum of two independent random variables is in $L^2$, is it true that both of them are in $L^1$?
Can you give an example s.t. $\mathbb E(X+Y)^2 < \infty$ but $\mathbb E X = \infty$ and $\mathbb E Y = \infty$?
May
12
comment 1D biased random walk - is the event of infinte many returns a tail event?
You should check Hewitt–Savage zero–one law - en.wikipedia.org/wiki/…
May
12
asked If the sum of two independent random variables is in $L^2$, is it true that both of them are in $L^1$?
May
7
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.
May
5
revised Simple probability problem?
typos
May
4
answered Simple probability problem?
Mar
10
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2
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Dec
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Nov
17
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 $\mathbb R$?
Nov
17
accepted The limit of integer valued random variables must be integer valued?
Nov
17
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?
Nov
17
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 $\infty \in \mathbb Z$?
Nov
17
asked The limit of integer valued random variables must be integer valued?
Nov
6
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Oct
24
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Sep
1
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Aug
31
comment Martingale with bounded increment.
@Did, I will remember to do that next time!