The price of a stock St follows geometric Brownian motion, with parameters and denoting the annualized rate of return and volatility. Suppose the current stock price is S0, and the risk-free interest rate is r (per annum). (i) Let Xt:=ertSt. Derive dXt. What kind of process is Xt ? What is E(X1) ? (ii) Derive the mean and variance of the stock price by the end of the third year, S3; and derive a 95% confidence interval for S3.((1.96)=0.975.)