(No R required for part 4b to 4f) Suppose that annual sales (in millions of dollars) of the Acme Corporation follow an AR(2) model: 2+ = 5 + 1.12t-1 – 0.5-2 + Wt, with 0 = 2. (a) Verify that this is a causal AR(2) model (you may use R to find the roots).(b) If sales for 2005, 2006, and 2007 were $9 million, $11 million, and $10 million, respectively, using one-step ahead prediction, forecast sales for 2008 and 2009.(c) Calculate 95% prediction intervals for your forecasts in part 4b.(d) Briefly explain, in words, why the prediction interval for the forecast in 2009 is wider than the prediction interval for the forecast in 2008.(e) If the sales in 2008 turned out to be $12 million, would this value surprise you?(f) Since we now know the sales for 2008 is $12 million, update your forecast for the year 2009.