There's a pretty thorough discussion on Wikipedia http://en.wikipedia.org/wiki/Two_envelopes_problem Suffice it to say that not everyone agrees. -- David
-----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Deepayan Sarkar Sent: Monday, August 25, 2008 4:35 PM To: Mario Cc: r-help@r-project.org; Greg Snow Subject: Re: [R] Two envelopes problem On Mon, Aug 25, 2008 at 1:51 PM, Mario <[EMAIL PROTECTED]> wrote: > No, no, no. I have solved the Monty Hall problem and the Girl's problem and > this is quite different. Imagine this, I get the envelope and I open it and > it has £A (A=10 or any other amount it doesn't matter), a third friend gets > the other envelope, he opens it, it has £B, now £B could be either £2A or > £A/2. He doesn't know what I have, he doesn't have any additional > information. According to your logic, he should switch, as he has a 50% > chance of having £2B and 50% chance of having £B/2. But the same logic > applies to me. In conclusion, its advantageous for both of us to switch. But > this is a paradox, if I'm expected to make a profit, then surely he's > expected to make a loss! This is why this problem is so famous. If you look > at the last lines of my simulation, I get, conditional on the first envelope > having had £10, that the second envelope has £5 approximatedly 62.6% of the > time and 37.4% for the second envelope. In fact, it doesn't matter what the > original distribution of money in the envelopes is, conditional on the first > having £10, you should exactly see 2/3 of the second envelopes having £5 and > 1/3 having £20. But I'm getting a slight deviation from this ratio, which is > consistent, and I don't know why. That has nothing to do with switching, and everything to do with properties of regression. Try: > env <- generateenv(r=2, rintexp, n=1e6, rate=1/10) > colMeans(env) [1] 15.76573 15.75436 > mean(env[which(env[,1] == 10) , 2]) # greater than 10 [1] 10.64476 > mean(env[which(env[,1] == 20) , 2]) # less than 20 [1] 18.10053 And now with a distribution with mean less than 10 > env <- generateenv(r=.5, rintexp, n=1e6, rate=1/10) > colMeans(env) # mean less than 10 [1] 7.881469 7.873117 > mean(env[which(env[,1] == 10) , 2]) [1] 8.966886 -Deepayan ______________________________________________ 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.
