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(1) Using the shell program lab1.m, write a program that will take an individual sample value as the input and will return the posterior probabilities and the value of g(x2)

(3.) Identify the class labels for the feature values using your program, and indicate their respective posterior probabilities and discriminant function values: x1 = [3.3, 4.4, 5.0, 5.7, 6.3]

lab1.m

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % ELE 888/ EE 8209: LAB 1: Bayesian Decision Theory %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [posteriors_x,g_x]=lab1(x,Training_Data)

% x = individual sample to be tested (to identify its probable class label) % featureOfInterest = index of relevant feature (column) in Training_Data % Train_Data = Matrix containing the training samples and numeric class labels % posterior_x = Posterior probabilities % g_x = value of the discriminant function

D=Training_Data;

% D is MxN (M samples, N columns = N-1 features + 1 label) [M,N]=size(D); f=D(:,1); % feature samples la=D(:,N); % class labels

%% %%%%Prior Probabilities%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Hint: use the commands "find" and "length"

disp('Prior probabilities:'); Pr1 = Pr2 =

%% %%%%%Class-conditional probabilities%%%%%%%%%%%%%%%%%%%%%%%

disp('Mean & Std for class 1 & 2'); m11 = % mean of the class conditional density p(x/w1) std11 = % Standard deviation of the class conditional density p(x/w1)

m12 = % mean of the class conditional density p(x/w2) std12= % Standard deviation of the class conditional density p(x/w2)

disp(['Conditional probabilities for x=' num2str(x)]); cp11= % use the above mean, std and the test feature to calculate p(x/w1)

cp12= % use the above mean, std and the test feature to calculate p(x/w2)

%% %%%%%%Compute the posterior probabilities%%%%%%%%%%%%%%%%%%%%

disp('Posterior prob. for the test feature');

pos11= % p(w1/x) for the given test feature value

pos12= % p(w2/x) for the given test feature value

posteriors_x=

%% %%%%%%Discriminant function for min error rate classifier%%%

disp('Discriminant function for the test feature');

g_x= % compute the g(x) for min err rate classifier.