Roughly sketch the shapes of the following Gaussians

The covariance matrix of Y is 4 3 0 Z = (3 6 0) 0 0 5 Which of the following variables are uncorrelated? Y1 and Y2 Y1 and Y3 Y2 and Y3 (Y1, Y3) and Y2 Y1 and 3Y1 + 4Y2 2Y3 What needs to be true about the variables to say they are independent, not just uncorrelated? rthpD-gn 2. Contour of bivariate Gaussian. Sketch the contour defined by f(x, y) = 0.06, where f(x, y) is the bivariate normal density with (a) Ax = 1, My = 2,02 = 03 = 1 and pry = 0. (b) Hz = 0, My = 0, 03 = of = 1 and Pry = 0.2. (c) #x = 0, My = 0,02 = 07 = 1 and Pxy = 0.8. (d) Ax = 0, My = 0,02 = 4, 0% = 1 and pry = 0.8. Here, o2 := VarX, o2 := VarY, and the correlation coefficient is defined as Pry := E(X -HI) ( Y-Hy) What is the distribution of X - Y, when (X, Y) has each of the bivariate distributions given above?2. Contour of bivariate Gaussian. Sketch the contour defined by f(x, y) = 0.06, where f(x, y) is the bivariate normal density with (a) Ax = 1, My = 2,02 = 03 = 1 and pry = 0. (b) Hz = 0, My = 0, 03 = of = 1 and Pry = 0.2. (c) #x = 0, My = 0,02 = 07 = 1 and Pxy = 0.8. (d) Ax = 0, My = 0,02 = 4, 0% = 1 and pry = 0.8. Here, o2 := VarX, o2 := VarY, and the correlation coefficient is defined as Pry := E(X -HI) ( Y-Hy) What is the distribution of X - Y, when (X, Y) has each of the bivariate distributions given above?I Roughly sketch the shapes of the following Gaussians N (pt; 2). For each, you only need to Show a representative contour line which is qualitatively accurate (has approximately the right orlentaom for instance). a) p=(g) and2=(g 2 b) 1\" = (3) and E = (01.75 \"01.75)