[R] Two envelopes problem
Duncan Murdoch
murdoch at stats.uwo.ca
Tue Aug 26 14:15:09 CEST 2008
On 26/08/2008 7:54 AM, Jim Lemon wrote:
> Hi again,
> Oops, I meant the expected value of the swap is:
>
> 5*0.5 + 20*0.5 = 12.5
>
> Too late, must get to bed.
But that is still wrong. You want a conditional expectation,
conditional on the observed value (10 in this case). The answer depends
on the distribution of the amount X, where the envelopes contain X and
2X. For example, if you knew that X was at most 5, you would know you
had just observed 2X, and switching would be a bad idea.
The paradox arises because people want to put a nonsensical Unif(0,
infinity) distribution on X. The Wikipedia article points out that it
can also arise in cases where the distribution on X has infinite mean:
a mathematically valid but still nonsensical possibility.
Duncan Murdoch
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