Advanced Random Walk Question (bruce, pzhon)

[gaming_mouse]

We know that if the random variable X represents the distance from the origin after a random walk of N steps, then, for sufficiently large N, X is normal with mean 0 and SD sqrt(N).

But consider the different but related random variable Y, which represents the maximum distance from the origin over the entire walk. That is, the farthest away from 0 that we ever get at any point during the N steps.

What is the distribution of Y?