1) Assume that we shoot with an artillery gun. let (Xth) denote the impact point on the ground of the i-th shell we shoot. The canon tube points always in the same direction and we shoot under the same circumstances with the same ammunition. Hence, X1 = (X11Y1)5X2 = (X2533): - - ' aX'n, =(Xn1Yn) are ii.d random vectors. Assume that we get the following 10 impact points Xi Yi 4.58 0.1 1.06 3.58 0.38 6.55 2.06 12.84 2.82 2.75 2.57 5.04 3.15 10.31 2.93 5.67 1.90 4.07 1.76 3.08 a) What is the center of gravity? Estimate E [X] and E [Y] b) Plot the data in two dimensions by hand. Without calculating anything but just looking at the data try to determine approximately the principal direction (eigenvectors) of the covariance matrix and the eigenvalues. c)Estimate the covariance matrix. d) Calculate the Principal Components of the estimated covariance matrix. From which direction is the canon shooting