(You may need a bit of help with this one.) Take a random walk process as specified in the form (2) of Section 8.4 in the text. You are now at time 0, and you know B0.

(i) What is the predicted value of B1? What is the variance of the prediction, that is, the variance of the discrepancy between your predicted value and the actual outcome?

(ii) Do the same for B2 at time 2. Predict the value knowing only B0 at time 0, so you have to form the best predictor available and then find its variance, conditional on the information available at time 0.

(iii) Carry it on until some time T in the future. How does the predictive variance accumulate as the horizon T gets larger and larger?