[Total: 16 marks] a) [7 marks] A time series with a periodic component can be constructed from X = uj sin(2avot) + u2 cos(2avot) where uj,u2 are independent random variables with zero means and E(uf ) = E(u;) =62 . The constant Vo determines the period or time it takes for the process to make one complete cycle. Show that this series is weakly stationary with autocovariance function y(h) = 0 cos(2avgh)