/[gzz]/manuscripts/Sigs/birthday.py
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revision 1.3 by tjl, Mon May 19 19:52:24 2003 UTC revision 1.4 by tjl, Mon May 19 19:58:25 2003 UTC
# Line 4  def log2birthdayprob(n, k): Line 4  def log2birthdayprob(n, k):
4      """return log2(p(k balls thrown to n bins, all end up alone))      """return log2(p(k balls thrown to n bins, all end up alone))
5      """      """
6      return (      return (
7              (n+.5) * log(n)              (n-k+.5) * (log(n) - log(n-k))
             - (n-k+.5) * log(n-k)  
8              - k              - k
             - k * log(n)  
9              ) / log(2)              ) / log(2)
10    
11  print log2birthdayprob(41, 31)  print log2birthdayprob(41, 31)
# Line 15  print log2birthdayprob(41, 21) Line 13  print log2birthdayprob(41, 21)
13  print log2birthdayprob(41, 11)  print log2birthdayprob(41, 11)
14  print log2birthdayprob(41, 2)  print log2birthdayprob(41, 2)
15  print log2birthdayprob(2L**56, 2L**23)  print log2birthdayprob(2L**56, 2L**23)
16    
17    for k in [20, 23]:
18        for n in [56, 60]:
19            print n,k,log2birthdayprob(2L**n,2L**k)
20    

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