random integer weirdness

*To*: mathgroup at smc.vnet.net*Subject*: [mg35772] random integer weirdness*From*: mark at markfisher.net (Mark Fisher)*Date*: Tue, 30 Jul 2002 07:22:27 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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.