Problem 1 ( 190 70 ) : In a 1 - D , 2 - class problem , the density functions of both classes are adequately represented by univariate Gaussians ,...

Pattern Recognition with Bayesian Decision Theory

Problem 1 ( 190 70 ) : In a 1 - D , 2 - class problem , the density functions of both classesare adequately represented by univariate Gaussians , with 1 = 4 , 01 = 2 12 6 , 02 - 3( 1 ) ( 15 / 10 ) Sketch the two density functions on the same figure using pencil andpaper ( i . e . , without MAIL AB or any other software package ) . Assume equalprior probability predict how many decision regions there would be( 2 ) ( $5/ 30 ) Assume equal prior probabilitya . ( 10 /5 ) If * = 4 .7 , which class does * belong to ? Use the MAP method .Show detailed stepsb . ( 15/10 ) Find the decision boundary using analytical methods instead ofthe sketchC . ( 10/5 ) Write an expression for the probability of error plerror co , )that an error occurs given that the truth is class Id . ( 20/10 ) Solve for the overall probability of euroSolve for the overall probability of euro( 3 ) ( 30 /20) Assume that P (1 ) = 0 .6 , P (2 ) = 0.4a . ( 20/ 10 ) Use MATLAB to draw the pat and the posterior probabilityComment on the differenceb . ( 5/ 5 ) Redo question 2 ( a )C . ( 5/ 5 ) Under what condition that there would just be one decisionregion and two decision regions ?