You have 1000 dollars to put in an account with interest rate R, compounded annually. That is,

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You have 1000 dollars to put in an account with interest rate R, compounded annually. That is, if Xn is the value of the account at year n, thenXn 1000 (1 + R)", = for n = 0, 1, 2,...

The value of R is a random variable that is determined when you put the money in the bank, but it does not not change after that. In particular, assume that R ∼ Uniform(0.04, 0.05).

a. Find all possible sample functions for the random process {Xn,n = 0, 1, 2, . . .}.

b. Find the expected value of your account at year three. That is, find E[X3].

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