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?
(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?
