"Simon, Steve, PhD" wrote:
>
> In a message to EDSTAT-L, you wrote:
>
> >(3) The high-moment measures concentrate on extreme tails if these
> >exist, even though they may contain vanishingly few data. This is not
> >always what one wants - consider the St. Petersburg Paradox.
>
> Could you tell us (me and EDSTAT-L) what the St. Petersburg paradox is. My
> apologies if I missed it in earlier discussion in this thread.
OK. Say we play a game in which you pay me a sum of money (to be
determined in a few moments) and we then toss a coin. If it comes up
heads the first time I pay you $1 and we stop. If it comes up heads the
second time I pay you $2 and we stop. Each time the prize doubles. Now,
what should you pay me to make the game fair?
The answer is that _whatever_ you pay me, the game is in your favor,
because your expected win is $1/2 + $2/4 + $4/8 +...... which diverges
to infinity. However, if the game were to stop when the prize reached
the total wealth of the human race, it would be a swindle if I were to
charge you as much as $30 to play; almost all of the expected value
comes from games so "rich" that they could not be settled.
-Robert
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