Example 10.1: You have 1000 dollars to put in an account with an interest rate R compounded annually. That is, if Xi is the value of the account at year i, then X0 = 1000 and Xi = 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 change after that. In particular, R follows a uniform distribution between 0.04 and 0.05.
a. Find all possible sample functions for the random process {Xn = 0, 1, 2}.
b. Find the expected value of your account at year three. That is, find E[X].