3. Let (Btzo be a standard Brownian motion. Suppose that we model the price per share of some nancial product X in U.S. dollars by using the process Pt = eln(P0)+Bt, t 2 0, where t represents the time in months and P0 is the price of the product at time t = 0. Suppose that we buy 50 shares of X when the price per share is $1. Suppose that as soon as the total worth of our shares is equal to one million dollars, we sell all of our shares of X, otherwise we keep them (potentially) indenitely. Approximate the probability that we sell our shares of X (and thus become millionaires) no more than one year after acquiring the nancial product. N ate: at some point in your computations you should reduce the desired probability to an expression that involves the integral of a Gaussian density 1 _ iw )2 f e 2: daP I 271'02 over some innite interval I. Recall that you cannot compute such integrals by nding an explicit antiderivative! Instead please use a software of your choice (e.g. Mathematica, Matlab) or online resources (e.g. WolframAlpha) to get an approximate numerical value for the integral