In this problem, you will build classifiers based on Gaussian discriminant analysis. Unlike Home-work 1, you are NOT allowed to use any libraries for out-of-the-box classification (e. g.sklearn).You may use anything innumpyandscipy. The training and test data can be found on in the post corresponding to this homework. Don’t usethe training/test data from Homework 1, as they have changed for this homework. Submit yourpredicted class labels for the test data on the Kaggle competition website and be sure to includeyour Kaggle display name and scores in your writeup. Also be sure to include an appendix of yourcode at the end of your writeup.(a) Taking pixel values as features (no new features yet, please), fit a Gaussian distribution toeach digit class using maximum likelihood estimation. This involves computing a mean and acovariance matrix for each digit class, as discussed in lecture. Hint:You may, and probably should, contrast-normalize the images before using their pixelvalues. One way to normalize is to divide the pixel values of an image by thel2-norm of itspixel values.(b) (Written answer) Visualize the covariance matrix for a particular class (digit). How do thediagonal terms compare with the off-diagonal terms? What do you conclude from this?(c) Classify the digits in the test set on the basis of posterior probabilities with two different ap-proaches.