Let {X(t), t 0} be Brownian motion with drift coefficient and variance parameter 2. Suppose

Let {X(t), t ≥ 0} be Brownian motion with drift coefficient μ and variance parameter σ2. Suppose that μ>0. Let x > 0 and define the stopping time T

(as in Exercise 21) by T = Min{t : X(t) = x}

Use the Martingale defined in Exercise 18, along with the result of Exercise 21, to show that Var(T ) = xσ2/μ3 In Exercises 25 to 27, {X(t), t ≥ 0} is a Brownian motion process with drift parameter μ and variance parameter σ2.