1: Bivariate normal: inference on the correlation coefficient Assume that ( X , Y ) follow a bivariate normal distribution with E ( X ) = E ( Y ) = 0 and V a r ( X ) = V a r ( Y ) = 1 . The pdf of ( X , Y ) is given as f ( x , y | ) = 1 2 1 2 exp { x 2 2 x y + y 2 2 ( 1 2 ) } , where is the correlation coefficient for X and Y . Suppose that we observe n iid realizations of ( X , Y ) . That is, we observe: X Y x 1 y 1 x 2 y 2 x n y n Suppose that the ( X , Y ) data are given as: In [2]: #note the updated/corrected simulation set.seed(7309) mu = c(0,0) rho = 0 Sig = matrix(c(1,rho,rho,1), ncol = 2) n = 15 X = mvrnorm(n, mu, Sig) x = X[,1]; y = X[,2] 1 (a) [4 points] Plot the data. Calculate the correlation coefficient using cor() and store it in the variable c. In [3]: Student's answer(Top) c