Timeline for Exchangeable Bernoulli random variables with bounded summation implies negative correlation?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Nov 19, 2018 at 5:34 | comment | added | zxzx179 | @fedja Nice example! Thanks so much! | |
| Nov 19, 2018 at 5:05 | comment | added | Ilya Bogdanov | @fedja: Ah yes, you are right! | |
| Nov 19, 2018 at 2:29 | comment | added | Iosif Pinelis | @fedja : Very nice example. In fact, the random variables are even more correlated: $P(X_1=X_2=1)=\frac12\,\frac{n-2}n$ for $n\ge2$, I think. | |
| S Nov 19, 2018 at 1:58 | history | suggested | Amir Sagiv | CC BY-SA 4.0 |
irrelevant tag+ English
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| Nov 19, 2018 at 1:07 | comment | added | fedja | @IlyaBogdanov On the contrary. If $X_1=1$, it makes it almost certain that we are in case $1$, so the probability that $X_2=1$ gets close to $1$. More precisely, $P(X_1=1,X_2=1)=P(X_1=0,X_2=0)=\frac 12\frac{(n-1)(n-2)}{n^2}$, which is almost full correlation. | |
| Nov 18, 2018 at 23:04 | review | Suggested edits | |||
| S Nov 19, 2018 at 1:58 | |||||
| Nov 18, 2018 at 21:42 | comment | added | fedja | Consider the case when with probability $1/2$ random $m$ of them are $1$ and with probability $1/2$ random $n-m$ of them are $1$ where $m=n-1$, say. Then it looks to me like the correlations are rather positive for large $n$. | |
| Nov 18, 2018 at 20:40 | review | First posts | |||
| Nov 18, 2018 at 23:04 | |||||
| Nov 18, 2018 at 20:38 | history | asked | zxzx179 | CC BY-SA 4.0 |