Random walks probability

Discussion in 'Math' started by boks, Feb 13, 2009.

  1. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0
    For a random walk of 10 000 steps, what is the chance of ending up exactly where we started?


    (10 000 choose 5000)/2^10000, right? This calculation can't be done on a calculator, so I use Stirling's formula:

    ln M! = M lnM - M + 0.5 ln (2*pi*M), knowing that

    (10 000 choose 5000) = 10 000!/(5000! * 5000!)

    But I also need a way to approximate 2*10 000. How do I do that?
     
  2. Papabravo

    Expert

    Feb 24, 2006
    10,135
    1,786
    Use logarithms
     
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