MathGroup Archive 2002

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random integer weirdness


There is some real weirdness with Random[Integer, j] for some large
values of j but not others (for both 4.1 and 4.2 versions).

<<Statistics`
n = 1000;
sim = Table[{j, (2/2^j) * Mean[Table[Random[Integer, 2^j], {n}]]}, 
      {j, 45, 65, 1/8}];
ListPlot[sim];

All the points should be near one if the random number generator were
working properly. What gives? Is this just a (very stark) symptom of
what Daniel Lichtblau mentioned in his May 2000 post?

>> The other failure only is apparent in very large big
>> integers, and I do not know exactly how to categorize it.

I just find this very troubling.

--Mark.


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