Unbias a random generator
Unbias a random generator is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Given a weighted one bit generator of random numbers where the probability of a one occuring, , is not the same as , the probability of a zero occuring. The probability of the occurrence of a one followed by a zero is , which is the same as the probability of a zero followed by a one: .
Task Details
- Use your languages random number generator to create a function/method/subroutine/... randN that returns a one or a zero, but with one occurring, on average, 1 out of N times, where N is an integer from the range 3 to 6 inclusive.
- Create a function unbiased that uses only randN as its source of randomness to become an unbiased generator of random ones and zeroes.
- For N over its range, generate and show counts of the outputs of randN and unbiased(randN).
Python
<lang python>from __future__ import print_function import random
def randN(N):
" 1,0 random generator factory with 1 appearing 1/N'th of the time" choose = [1] + [0] * (N-1) def rand(): return random.choice( rand.choose ) rand.choose = choose return rand
def unbiased(biased):
'uses a biased() generator of 1 or 0, to create an unbiased one' this, that = biased(), biased() while this == that: # Loop until 10 or 01 this, that = biased(), biased() return this # return the first
if __name__ == '__main__':
from collections import namedtuple
Stats = namedtuple('Stats', 'count1 count0 percent')
for N in range(3, 7): biased = randN(N) v = [biased() for x in range(1000000)] v1, v0 = v.count(1), v.count(0) print ( "Biased(%i) = %r" % (N, Stats(v1, v0, 100. * v1/(v1 + v0))) )
v = [unbiased(biased) for x in range(1000000)] v1, v0 = v.count(1), v.count(0) print ( " Unbiased = %r" % (Stats(v1, v0, 100. * v1/(v1 + v0)), ) )</lang>
Sample output
Biased(3) = Stats(count1=331800, count0=668200, percent=33.18) Unbiased = Stats(count1=499740, count0=500260, percent=49.973999999999997) Biased(4) = Stats(count1=249770, count0=750230, percent=24.977) Unbiased = Stats(count1=499707, count0=500293, percent=49.970700000000001) Biased(5) = Stats(count1=199764, count0=800236, percent=19.976400000000002) Unbiased = Stats(count1=499456, count0=500544, percent=49.945599999999999) Biased(6) = Stats(count1=167561, count0=832439, percent=16.7561) Unbiased = Stats(count1=499963, count0=500037, percent=49.996299999999998)