Problem 2: Let X and Y be two independent random variables with E(X) = 1, E(Y) = 0, Var(X) = 4, Var(Y) = 2. Let W = 2X + Y +1 and Z = 3X +Y. a) Find the expect ed value of W, the expected value of Z. b) Find the variance of W. c) Find the covariance of Z and W.

Suppose X and Y are independent random variables with E(X) =2, E(Y)=3,V(X)=4,V(Y)=16. Finda)E(5X-Y) b)V(5X-Y) c)COV(3X+Y,Y) d)COV(X,5X-Y)

Consider an MA(2) model: STEPS -Write the equation of the M(2) model-Determine the model based on the delay operator.- Find the expected value of the model- Find the variance of the model.- Find the covariances associated with 1,2, and s steps.- Find the associated correlation indices of 1,2, and s steps.- Assume that information is available up to time $h$ and the function that contains the accumulated information f(h, h-1,……), determine the forecasts and the error associated with 1,2, and s steps.