Part I Single Feature

$1.$ Create a matlab script that will perform each of the steps required for this exercise.

$2.$ Load $$partOneData$.$mat$$ into the matlab environment $($included in blackboard as part of the

assignment$).$

$3.$ Create a histogram for each of the class distributions $\{$classOne$,$ classTwo$\}.$ Plot each of the

histograms on the same figure $($use $100$ bins$).$ The figure should contain a title, legend and the x

and y axis should be labeled appropriately.

$4.$ Report the prior probability of classOne? $($Hint: Number of classOne samples divided by all

samples$)$

$5.$ Report the prior probability of classTwo? $($Hint: see above hint, but for classTwo$)$

$6.$ Create a random partition of the data, splitting each of the classes into $60\%$ training and $40\%$

testing.

a$.$ Using only the training data, find the maximum likelihood estimator for the following

parameters:

i$.$ Class One: $,\backslash$sigma Part I Single Feature

Create a matlab script that will perform each of the steps required for this exercise.

Load 'partOneData.mat' into the matlab environment $($included in blackboard as part of the

assignment$).$

Create a histogram for each of the class distributions $\{$classOne$,$ classTwo$\}.$ Plot each of the

histograms on the same figure $($use $100$ bins$).$ The figure should contain a title, legend and the $x$

and y axis should be labeled appropriately.

Report the prior probability of classOne? $($Hint: Number of classOne samples divided by all

samples$)$

Report the prior probability of classTwo? $($Hint: see above hint, but for classTwo$)$

Create a random partition of the data, splitting each of the classes into $60\%$ training and $40\%$

testing.

a$.$ Using only the training data, find the maximum likelihood estimator for the following

parameters:

i$.$ Class One: $,$

ii$.$ Class Two: $,$

b$.$ Classify each of the samples in the test partition using a Bayesian classifier $($you must

create a function that will do this$).$ Report the prediction accuracy for class one and class

two.

Hint: You will need to create a method that, given the mean and standard deviation of a

distribution, determines the probability that $\text{'}x\text{'}$ belongs to the distribution.

Matlab template below:

function probability $=$ computeGaussianDensity$($mean$,$ stdDev, $x$

$($Your code to calculate the Gaussian density here$)$