[R] Two envelopes problem

[Jim Lemon]

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