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Except that your logarithms can have any consistent base, including 2.

So I don't think using a logarithm to introduce a special dependence on e is warranted in this case.



Well the expected value of E[log2(rand())] is not the same as E[log(rand())] and therein lies the difference. See my sibling comment.

Like I said, you can check this in a python terminal.




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