Timeline for Coin flipping and a recurrence relation
Current License: CC BY-SA 2.5
9 events
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| Feb 17, 2011 at 10:20 | comment | added | Louigi Addario-Berry | @Didier PS though I wasn't being shy (not one of my strong points), I have followed your suggestion and made the argument of the second paragraph more explicit. | |
| Feb 17, 2011 at 10:19 | history | edited | Louigi Addario-Berry | CC BY-SA 2.5 |
Followed a suggestion from the comments.
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| Feb 17, 2011 at 10:12 | comment | added | Louigi Addario-Berry | @Didier, yes, T is a sum of exponentials, and its renormalized distribution is the Gumbel distribution. (In fact, if I recall correctly this is Gumbel's original example.) | |
| Feb 17, 2011 at 7:37 | comment | added | Did | @Louigi Minor point: first line of second paragraph, cancel the upper part sign around $T$. Re $H_n$, I find this modified version of your post a bit mysterious, since your parenthesis seems to give a stronger result than what you write before the parenthesis, thus the reader is led to wonder whether this stronger result holds or not... No reason to be shy here! Indeed, $T$ IS a sum of exponentials in the sense that $T=X_1/1+X_2/2+\cdots+X_n/n$ where $(X_i)$ is an i.i.d. sequence of standard exponential random variables. (Nice post, by the way.) | |
| Feb 16, 2011 at 18:52 | history | edited | Louigi Addario-Berry | CC BY-SA 2.5 |
Deleted the false part of my answer.
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| Feb 16, 2011 at 18:48 | comment | added | Louigi Addario-Berry | Oh, you're right Didier, that step was nonsense. I'll fix my answer. | |
| Feb 16, 2011 at 17:52 | comment | added | Did | @Louigi: The maximum of $n$ standard (independent) exponentials is again distributed as an exponential... Sure about this? | |
| Feb 16, 2011 at 17:08 | history | edited | Louigi Addario-Berry | CC BY-SA 2.5 |
Added a little detail in the last equation.
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| Feb 16, 2011 at 16:30 | history | answered | Louigi Addario-Berry | CC BY-SA 2.5 |