15.10 If Bt is a Brownian motion and Xt = eBt , for some > 0,...

15.10 If Bt is a Brownian motion and Xt = eσBt , for some σ > 0, calculate the pdf of Xt. Calculate E[Xt] and V(Xt). Calculate the transition probability P(Xt ≤ y | Xt0 = y0), and give the density of this transition probability. For this part, use the functions in Definition 15.2.