(20 points) Suppose a stock price S has an expected return ( of 12% per annum, a volatility o of 20% per annum and that the risk-free rate is 5%. Suppose that the stock price follows the usual stochastic process (Geometric Brownian motion) with these u and o. Suppose today the stock price is $100. (a) (10 points) What is the probability distribution for In(S,) at T = 1.5 years? Prove your result using Ito's Lemma. (b) (5 points) What is the probability that the stock price lies between 140 and 90 in 18 months? (c) (5 points) Find the 95% confidence interval (the one with midpoint at the expected value)for the stock in 18 months