Suppose that X1, X2, is a lognormal geometric random walk with parameters = 0.1, = 0.2.

1. Find P(X3 > 1.2Xo).

2. Find the conditional variance of Xk/k given Xo for any k.

3. Find the minimum number of days before the probability is at least 0.9 of doubling one's money, that is, find the small value of t such that P(Pt/Po 2) 0.9.