5. In this exercise we will prove that a random walk is nonstationary. Let Y = Y-1+u for t = 1,...T where Yo = 0 and u, is i.i.d. with mean 0 and variance 2 (a) Show that Y = Yo+u. Hint: Write down the expressions for the first few values of Y in terms of Yo and u's (e.g. Y, Y2,Y3 in terms of Yo and u, U2, u3), then look at the pattern and come up with a general expression for Y, in terms of Yo and u's. (b) Compute the mean and variance of Y (c) Use the result in part (b) to explain why Y, in nonstationary.