Let P(x | C;) ~ N(;, ) for a two-category, one-dimensional classification problem with classes C1...

 

Transcribed Image Text:

Let P(x | C;) ~ N(;, ) for a two-category, one-dimensional classification problem with classes C1 and C2, P(C) = P(C2) = 1/2, and > . (a) Find the Bayes optimal decision boundary and the corresponding Bayes decision rule. (b) The Bayes error is the probability of misclassification, Pe = P((misclassified as C) | C2) P(C2) + P((misclassified as C2) | C) P(C). Show that the Bayes error associated with this decision rule is where a = M2-M1 20 Pe= e 212 dz Activate Win Let P(x | C;) ~ N(;, ) for a two-category, one-dimensional classification problem with classes C1 and C2, P(C) = P(C2) = 1/2, and > . (a) Find the Bayes optimal decision boundary and the corresponding Bayes decision rule. (b) The Bayes error is the probability of misclassification, Pe = P((misclassified as C) | C2) P(C2) + P((misclassified as C2) | C) P(C). Show that the Bayes error associated with this decision rule is where a = M2-M1 20 Pe= e 212 dz Activate Win