(afor li ( show that (xi yi lies exactly on the decision border (bfor li show that (xi yi lies strictly inside the margins (cshow that for li the point (xi yi lies outside the margins and is correctly classified well-known data set is the mnist handwritten digit databasecontaining many thousands of digitalized numbers (from to )each described by matrix of gray scales similar but much smaller data set is described in [ hereeach handwritten digit is summarized by matrix with integer entries from (whiteto (blackfigure shows the first digitized images the data set can be accessed with python using the sklearn package as follows from sklearn import datasets digits datasets load_digits (x_digits digits data explanatory variables y_digits digits target responses figure classify the digitized images (adivide the data into training set and test set (bcompare the effectiveness of the -nearest neighbors and naive bayes method to classify the data (cassess which to use in the -nearest neighbors classification download the winequality-red csv data set from uci' wine-quality website the response here is the wine quality (from to as specified by wine "expertand the explanatory variables are various characteristics such as acidity and sugar content use the svc classifier of sklearn svm with linear kernel and penalty parameter (see remark to fit the data use the method cross_val_score from