[R] Two envelopes problem
Jim Lemon
jim at bitwrit.com.au
Tue Aug 26 13:40:12 CEST 2008
Hi Mario,
If I understand your problem statement, the random choice of one of the
two envelopes ensures that the probability of choosing one or the other
is 0.5. If you find 10 (units, I can't find the pound symbol on this
keyboard), there is an equal likelihood that the other envelope contains
5 or 20 units. Your expected value for the swap is thus 7.5*0.5 + 15*0.5
= 11.25 units. The trick is in the "twice as much, half as much"
statement. If it was x units more or less, a symmetric distribution,
swapping wouldn't make any difference.
Jim
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