5. Consider the following table showing the joint probability of the value of the S&P 500 and per capita GDP: Y = Value of the S&P 500 $8,000 $10,000 $0 0.2 0.1 0.3 X = Per Capita GDP $25,000 0.1 0.2 0.3 $50,000 0.1 0.3 0.4 0.4 0.6 (a) What is the expected value of the S&P 500? (b) What is the standard deviation of the S&P 500? (c) Is per capita GDP independent of the value of the S&P 500? (d) What is the covariance of per capita GDP and the value of the S&P 500