1.1. Consider the simple random walk

in which the summands are independent with Pr{ = ± 1 } = 2I n III, Section 5.3, we showed that the mean time for the random walk to first reach -a 0 is ab. Use this together with the invariance principle to show that E[T] = ab, where T = Ta.h = min(t ? 0; B(t) = -a or B(t) = b}, and B(t) is standard Brownian motion. Hint: The approximate Brownian motion (1.11) rescales the random walk in both time and space.

S = + S = 0,