Question: 3. (a) Let { B : t > 0} be a standard Brownian Motion. Let 0 0} is a standard Brownian Motion. If / =

3. (a) Let { B : t > 0} be a standard Brownian Motion. Let 0 0} is a standard Brownian Motion. If / = 4 ando = 3 for t = 1, 2,3 and p = 3 ando = 5 for t = 4, 5, 6, and So = 3; find the probability distribution of $6. [4] (c) For a > 0 and { Bt : t > 0} a standard Brownian Motion, let Xt = Bat/ va, for t 2 0. Is Xt a Brownian Motion? [5] This question is worth 14 marks. 4. Suppose that the stock price S, follows a Geometric Brownian Motion with parameter / and o. Find Eo [(ST ) " ] (6 marks)

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