30 Oct
2007
30 Oct
'07
12:55 p.m.
he probabiity that a random walk (with probabiity p of stepping to the left) will, starting form 0, ever reach a negative number is L = (1-sqrt(1-4pq)) / 2q, which simplifies to L = (1-|2p-1|) / 2(1-p). Considering the cases p >= 1/2 and p <= 1/2 separately: ------------------------------- L(p) = 1 if p >= 1/2, and L(p) = p/(1-p) if p <= 1/2. ------------------------------- I find this highly bipartite behavior rather amusing. --Dan