Biased random?

[Ivan Voras]

Jeffrey Barish wrote:

> If you take the difference between two uniformly distributed random
> variables, the probability density function forms an isosceles triangle
> centered at 0.  Take the absolute value of that variable and the pdf is a
> straight line with maximum value at 0 tapering to 0 at max.  Thus,
> 
> z = abs(randint(0, max) - randint(0, max))
> 
> ought to do the trick.

It's elegant :)

I've noticed something interesting in my test: the value 0 appears less
often than other values (which behave as they should). I wrote this test
script:

from random import randint

map = {}
for x in xrange(11):
        map[x] = 0

for a in xrange(500):
        x = abs(randint(0, 10) - randint(0, 10))
        map[x] += 1

print map

and here are some results:

> python a.py
{0: 49, 1: 66, 2: 72, 3: 73, 4: 64, 5: 55, 6: 40, 7: 36, 8: 18, 9: 18,
10: 9}
> python a.py
{0: 34, 1: 90, 2: 77, 3: 61, 4: 56, 5: 52, 6: 42, 7: 34, 8: 27, 9: 15,
10: 12}
> python a.py
{0: 33, 1: 80, 2: 84, 3: 62, 4: 52, 5: 46, 6: 51, 7: 31, 8: 35, 9: 16,
10: 10}
> python a.py
{0: 50, 1: 100, 2: 69, 3: 53, 4: 63, 5: 47, 6: 41, 7: 26, 8: 30, 9: 11,
10: 10}
> python a.py
{0: 31, 1: 84, 2: 70, 3: 70, 4: 74, 5: 50, 6: 38, 7: 28, 8: 31, 9: 15,
10: 9}
> python a.py
{0: 43, 1: 101, 2: 79, 3: 66, 4: 41, 5: 59, 6: 37, 7: 30, 8: 26, 9: 15,
10: 3}
> python a.py
{0: 44, 1: 108, 2: 74, 3: 50, 4: 53, 5: 54, 6: 39, 7: 34, 8: 28, 9: 13,
10: 3}
> python a.py
{0: 42, 1: 72, 2: 70, 3: 72, 4: 61, 5: 54, 6: 41, 7: 36, 8: 30, 9: 15,
10: 7}

If I ignore the case when the delta is 0, it works fine, but I don't
understand why should the 0-case happen less often than others.


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