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(1) Let X have N(0, 1) distribution, call it P. Let Y = X +2. Find the probability measure so that Y has N(0,

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(1) Let X have N(0, 1) distribution, call it P. Let Y = X +2. Find the probability measure so that Y has N(0, 1) distribution under Q. Give the derivative dQ/dP. Give the distribution of X under Q. (2) Let Bt, t0, be Brownian motion started at 0 under probability P. Let X = 2B+4t. Give he probability measure Q so that X is a martingale on [0,T]. Specify the derivative dQ/dP.

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