Python multi-part question

  • Problem 2.2 page 47

2.2 In a two-class one-dimensional problem the pdf’s are the Gaussians N(0,a2)and
,V(1. c 2 )for the two classes, respectively. Show that the threshold xu minimizing
the average risk is equal to

where h 11 = A22 = 0 has been assumed

  • Problem 2.5 page 47

Consider a two (equiprobable) class one-dimensional problem with samples distrihuted according to the Rayleigh pdf in each class, that is,

Compute the decision boundary point g ( x ) = 0

  • Problem 2.7 page 48

2.7 In a three-class two-dimensional problem the feature vectors in each class are
normally distributed with covariance matrix

The mean vectors foreachclass are [O. 1,O.1IT, [2.1, 1.9IT, [- 1.5, 2.OlT. Assuming
that the classes are equiprobable, (a) classify the feature vector [1.6, 1S I T according
to the Bayes minimum error probability classifier; (b) draw the curves of equal
Mahalanobis distance from [2.1, 1.9IT



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