Problem 1. Consider a family of 1-dimensional class-conditional densities given by: p(r|w;) = 604 exp where 0; is the parameter corresponding to class wi. (a) Given independent samples r1, #2, · ··...

Extracted text: Problem 1. Consider a family of 1-dimensional class-conditional densities given by: p(r|w;) = 604 exp where 0; is the parameter corresponding to class wi. (a) Given independent samples r1, #2, · ·· ,In from class wi, find the maximum like- lihood estimate of 0;. (b) Suppose that we have two classes, i.c., C = 2. We have observed the samples Di = {1,2,6, 7} from class wi and D2 = {9,13, 14} from class w2. ASsuming that P(wi) = and using the maximum likelihood estimates of 01 and 02, find the Bayes' classifier and determine the decision regions R1 and R2.