How is the solution showing Cov(X_t, X_t+20) = (t+20)*Sigma^2... I believe the solution should be (t-20)*sigma^2 as there are a finite number of variables and the X's are independent. Kindly guide where is my understanding incorrect?
Just had a look at the examiner's report (I assume that's what you mean by the solution?) That's not what it says. It says that Cov(Y_t, Y_(t+20)) = t * sigma^2. This makes sense because Y_t and Y_(t+20) are made up of iid X_i terms each having variance sigma^2, and they overlap for 't' of these terms. Then the solution shows how to calculate the correlation from the covariance using the formula for (Pearson) correlation.
