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Please answer both parts of the problem. Thank you in advance!

Problem 4: 10 points Recall that for a normally distributed X ~ 11, ?2j, its moment generating function is: My (u) = EPI = emutaw, for any u. Suppose that a Gaussian process, X = {X(t) : t 0) , is presented as where B-(B(t) : t-0} is a standard Brownian motion. A process, Y(t)-ex(t), s known as geometric Brownian motion 1. Find the expected value of Y (t). 2. Find the variance of Y (t) Present your answers in algebraic form and simplify them.

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wiotio n ie.ECeo 2X (t 2 2 大 0:2 2 (七) 2 264

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