Let's call the two envelopes A and B. Now envelope A could have X or A could have 2X and likewise B could have X or B could have 2X. Those are all the possible outcomes so by the definition of a sample space our sample space is [A,B] where A is the set [X,2X] and B is the set [X,2X], which means our sample space could also be written as [[X,2X],[X,2X]]. — Jeremiah
...which of 5 and 20 is even a possible value of X — Srap Tasmaner
If it's heads you put a red ball in one box and a blue ball in a second box. If it's tails you put a red ball in one box and a green ball in a second box. — Michael
E(U)=P(U=x)(x)+P(U=2x)(2x) — Srap Tasmaner
See how red blue and green are all mentioned by name as possibilities. — Srap Tasmaner
There is not nearly enough information available to base a decision on. — Srap Tasmaner
The distribution in the other letter cannot be [Y/2, 2Y] as one of those values simply does not exist. You have still created a sample space with impossible outcomes. The truth is that Y is not usable information. The error is making new assumptions based on Y. — Jeremiah
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