Expected time in a bracket

(a) Prove $\mathbb E\tau=ab/\sigma^2$ for the driftless bracket, including the argument that $\mathbb E\tau<\infty$. (b) A Nifty futures scalper uses a 200-point stop and a 200-point target with daily volatility 240 points. What is the expected holding time in trading days, and in hours of a 6.25-hour session (assume volatility is uniform through the session)? (c) What if the target is moved to 400 points?