Messages in this thread | | | Subject | Re: /dev/random vs. /dev/urandom | From | "Patrick J. LoPresti" <> | Date | 08 Jan 2005 12:34:30 -0500 |
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linux-os <linux-os@chaos.analogic.com> writes:
> In this case I AND with 1, which should produce as many '1's as > '0's, ... and clearly does not.
Actually, a fair coin flipped N times is unlikely to come up heads exactly N/2 times, and the probability of this drops quickly as N grows.
What is true is that it will usually come up heads N/2 times, give or take sqrt(N). Mathematicians call this the "Central Limit Theorem".
For example, take N=32. The square root of 32 is a little less than 6. So we expect to see between 16-6 (i.e., 10) and 16+6 (i.e., 22) heads in a typical trial. (Of course, in one trial out of 4 billion it will come up all heads. The Central Limit Theorem is about "usual" outcomes, not every outcome.)
So we expect between 10 and 22 odds/evens in your trial.
> Trying /dev/random > 0100000101010000010001000101000000000000000101000100010000000101 > odds = 14 evens = 18 > Trying /dev/urandom > 0001010001000100000101000100010001000000000000000000010000000000 > odds = 10 evens = 22 > LINUX> ./xxx > Trying /dev/random > 0100000100010101000101010101010101000100010000010001010000000101 > odds = 20 evens = 12 > Trying /dev/urandom > 0100000100000101010001000101010001010001000000010101010100010000 > odds = 18 evens = 14
Well how about that. Try it with larger N, and you will find it gets even harder to hit a case where the total is outside the sqrt(N) error margin. And of course, as a percentage of N, sqrt(N) only shrinks as N grows.
If you doubt any of this, try it with a real coin. Or read a book on probability.
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