Timeline for When does the law of large numbers fail?
Current License: CC BY-SA 3.0
19 events
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| Feb 27 at 22:47 | comment | added | gui11aume |
n=1; x=c(); while(TRUE) { n = n+1; x = c(x, runif(n=1, -n*2^n, n*2^n)); print(mean(x)) }
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| Feb 27 at 3:46 | comment | added | Uk rain troll | can someone make a demo/simulation in R that shows when the law of large number of fails? | |
| Jan 5, 2014 at 12:43 | history | edited | gui11aume | CC BY-SA 3.0 |
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| Dec 8, 2013 at 23:21 | history | edited | gui11aume | CC BY-SA 3.0 |
Expanded and corrected the example.
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| Jul 4, 2012 at 11:43 | vote | accept | emanuele | ||
| Jun 6, 2012 at 17:32 | comment | added | cardinal | If they are identically distributed, but not independent, the limit in question may not exist at all. | |
| Jun 6, 2012 at 17:19 | comment | added | gui11aume | @emanuele I edited the answer to clarify. 1/4 is the max variance of a Bernouilli 0-1 variable (its variance is $p(1-p)$). | |
| Jun 6, 2012 at 17:17 | comment | added | gui11aume | @cardinal, after giving it a thought, I think that they just need to be identically distributed for the formula to make sense. I edited accordingly because it fits better with what comes after. | |
| Jun 6, 2012 at 17:13 | history | edited | gui11aume | CC BY-SA 3.0 |
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| Jun 6, 2012 at 17:09 | comment | added | gui11aume | @cardinal, yup! I was thinking about the meaning of the terms in non IID case but could not come with anything satisfactory. | |
| Jun 6, 2012 at 17:07 | comment | added | cardinal | Thanks for the recent edit. I'd still suggest you clarify that the limiting statement only makes sense if the $X_k$ are iid and also that the right-hand side should be $P(X \in A)$ and not $P(A)$. | |
| Jun 6, 2012 at 17:05 | history | edited | gui11aume | CC BY-SA 3.0 |
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| Jun 6, 2012 at 16:42 | comment | added | cardinal | It is not clear what $1_A(X_k)$ means or how it relates to $P(A)$. If the $X_k$ are iid (that is, not just independent), then we might interpret the former as $1_{(X_k \in A)}$ and the latter as $P(X_1 \in A)$, but otherwise... | |
| Jun 6, 2012 at 16:39 | comment | added | emanuele | @gui11aume i don't understand "We see that the condition above will hold, because the variance of an indicator function is bounded above by 1/4.". What does it means? | |
| Jun 6, 2012 at 15:46 | comment | added | gui11aume | @whuber True. I focused too much on the title of the question. Thanks for pointing. I updated the answer. | |
| Jun 6, 2012 at 15:30 | history | edited | gui11aume | CC BY-SA 3.0 |
Added the part that starts with "Now, to specifically answer your question..."
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| Jun 6, 2012 at 14:53 | comment | added | whuber♦ | Are you two discussing the same law? The question asks about frequencies of events while this reply seems to focus on the sampling distribution of a mean. Although there is a connection, it hasn't yet appeared explicitly here as far as I can tell. | |
| Jun 6, 2012 at 14:13 | comment | added | emanuele | One comment. On wikipedia (lnl page) i have read that the non finiteness of variance only decelerate the convergence of the mean value. Is different from what you states? | |
| Jun 6, 2012 at 12:43 | history | answered | gui11aume | CC BY-SA 3.0 |