I need help studying for Theory of Finance, I cannot figure out this question.

Suppose that a stock price s follows geometric Brownian motion with ex- pected return u and volatility o: dS = u Sdt +oSdz. (16) Define the process Fas: F = sin (17) and its logarithm as: f = log(F), (18) where n is some constant. (a) [20 marks] What is the process followed by the variable F = Sn? (b) (20 marks] Show that F also follows geometric Brownian motion. (c) (20 marks] Find the law of motion equation df. Show the intermediate steps. (d) [40 marks] Suppose that in the first two years = 2 and o = 3 and for the next two years u = 3 and o = 4. If the initial value of the variable is So = 2 and n = 1 find: i. the expected value of S and F = S" after two years; ii. the probability distribution of f2 fo; iii. the probability distribution of f4 - fo; iv. the probability distribution of f4. Suppose that a stock price s follows geometric Brownian motion with ex- pected return u and volatility o: dS = u Sdt +oSdz. (16) Define the process Fas: F = sin (17) and its logarithm as: f = log(F), (18) where n is some constant. (a) [20 marks] What is the process followed by the variable F = Sn? (b) (20 marks] Show that F also follows geometric Brownian motion. (c) (20 marks] Find the law of motion equation df. Show the intermediate steps. (d) [40 marks] Suppose that in the first two years = 2 and o = 3 and for the next two years u = 3 and o = 4. If the initial value of the variable is So = 2 and n = 1 find: i. the expected value of S and F = S" after two years; ii. the probability distribution of f2 fo; iii. the probability distribution of f4 - fo; iv. the probability distribution of f4