10 Brownian motion is not going to be adequate as a stock market model. First, it has constant mean, whereas the stock of a company usually grows at some rate, if only due to inflation. Moreover, it may be too noisy' (that is the variance of the increments may be bigger than those observed for the stock) or not noisy enough. We can scale to change the noisiness' and we can artificially introduce a drift, but this still won't be a good model. Here is one reason why. Suppose that {W}t20 is standard Brownian motion under P. Define a new process {St}t20 by St = ut +oW where o > 0 and u E R are constants. Show that for all values of o > 0, u E R and T> 0 there is a positive probability that St is negative. 10 Brownian motion is not going to be adequate as a stock market model. First, it has constant mean, whereas the stock of a company usually grows at some rate, if only due to inflation. Moreover, it may be too noisy' (that is the variance of the increments may be bigger than those observed for the stock) or not noisy enough. We can scale to change the noisiness' and we can artificially introduce a drift, but this still won't be a good model. Here is one reason why. Suppose that {W}t20 is standard Brownian motion under P. Define a new process {St}t20 by St = ut +oW where o > 0 and u E R are constants. Show that for all values of o > 0, u E R and T> 0 there is a positive probability that St is negative