Question 3: An economist is trying to forecast the gross domestic product (GDP) of a small developing country. The GDP is described by Y=C+G+ I + X where the variables represent, consumption (C), government spending (G), investment (I), and net exports (X). The country's net exports are equal to $1 billion and the government spending was set at the beginning of the year at $2.5 billion. The values of consumption and investment are uncertain with the joint distribution below (Outcomes are in billions of dollars). I 10 5 0.2 10 C 15 0.05 15 0.05 0.05 0.2 0.1 20 0.05 0.1 0.2 (a) (2.5 points) Compute E(C), E(I) and Cov(C, I). (b) (2.5 points) Compute E(Y) and Var(Y). (c) (5 points) The economist would like to report the statistics in terms of their local currency instead of in dollars. Suppose 1 unit of the local currency is equivalent to 1/4 dollars, compute the expectation and variance of the GDP in billions of the local currency.