Given below is a bivariate distribution for the random variables x and y. f(x, y) X y 0.2 50 80 0.5 30 50 0.3 40 60 (a) Compute the expected value and the variance for x and y. E(X) = 39 X E(y) = 61 X Var(x) = 1570 X Var(y) = 3830 X (b) Develop a probability distribution for x + y. x+y f(x + y) 130 0.2 80 0.3 X 100 0.5 X (c) Using the result of part (b), compute E(x + y) and Var(x + y). E(x + y) = 100 X Var(x + y) = 10300 X (d) Compute the covariance and correlation for x and y. (Round your answer for correlation to two decimal places.) covariance 71 X correlation 0.97 X