Understanding average Brownian exit time

Let W denote Brownian motion starting from the origin. The idea of this paper is give a computation of the expected exit time E[tau][a,b] from an interval [a,b], where a<0<b, without the aid of Wald's Identity. Instead, the Strong Markov Property and other fundamental properties of Brownian motion are used directly to show that E[tau][a,b] is linear in both a and b, and then a limiting result about Brownian motion is used to compute the constant of linearity. As a part of the proof of the linearity of the expected exit time, we compute the distribution of W[tau][a,b].