Suppose we are allowed to observe a random process Z(r) at two points in time, ro and ri .
Based on those observations we would like to estimate Z(t) at time t = t2 where t0 1 2 . We can view this as a prediction problem. Let our estimator be a linear combination of the two observations,
(a) Use the orthogonality principle to find the MMSE estimator.
(b) Suppose that 
for positive constants b and c. Show that in this case, the sample at time t = to is not useful for predicting the value of the process at time t = t2 (given we have observed the process at time t = t1 > to ). In other words, show that a = 0 .