In this problem we will apply discriminant analysis to recognize the digits in the MNIST data set (http://yann.lecun.com/exdb/mnist/). As a bonus problem we will construct "Fisher digits". We will train our model using the training data sets ("train-images-idx3-ubyte.gz" and "train-labels-idx1-ubyte.gz") and test the performance using the test data set ("t10k-images-idx3-ubyte.gz" and "t10k-labels-idx1-ubyte.gz").

1. The images are 28 x 28 pixels in gray-scale. The categories are 0, 1, ... 9. We concatenate the image rows into a 28 x 28 vector and treat this as our feature, and assume the feature vectors in each category in the training data "train-images-idx3-ubyte.gz") have Gaussian distribution. Draw the mean and standard deivation of those features for the 10 categories as 28 x 28 images using the training images ("train-images-idx3-ubyte.gz"). There should be 2 images for each of the 10 digits, one for mean and one for standard deviation. We call those "mean digits" and "st