So if I put $10 and $20 into the envelopes, then told you that the values were multiples of $10, it would be wrong for you to assess probabilities on $100, $1,000,000 and so on? :-)
But what if you reasoned that there were far more multiples of 10 above 20 than below 20? What if I was really evil and the multiples of 10 that I always put in the envelopes were 0x$10 and 0x$10. When you opened an empty envelope, what are the odds the other has $1,000,000? What are the odds it has $10? It seems the information given can be misleading. Robert Farley Metro www.Metro.net -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Duncan Murdoch Sent: Tuesday, August 26, 2008 05:15 To: Jim Lemon Cc: r-help@r-project.org; Mario Subject: Re: [R] Two envelopes problem 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 ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
