Q2. In this question we consider a classification problem where C₁ = C2, π₁ = π2 andX|Y = 1 ~ N₂(0, 12), X|Y=2 ~ №₂ (µ, Σ)for some µ € R² and positive definite 2 × 2 matrix Σ.(a) In each of the following examples find the Bayes classifier and draw a diagram showing theshape of the regions R₁ and R₂. You may use any result from the notes, provided it is clearlystated.(i) µ = (1,1)T and Σ = I2(ii) μ = 0 and Σ = 212(iii) μ = 0 and 2 =(iv) µ = (0,−1)T and Σ = (39)=(ν) μ=(vi) με0 and Σ =20(²9)= 0 and Σ ==1/2)4(3 1/2)2(b) Assuming that µ = 0 and Σ ‡ I2, give a necessary and sufficient condition on Σ for the regionR₁ to be bounded. You may wish to use the Spectral Decomposition Theorem and separatelyconsider the cases λ2 > 1, №2 = 1 and λ2 < 1, where λ2 is the smallest eigenvalue of Σ.■

(a) (i) The Bayes classifier for this case would be a straight line that separates the two normal…

Answered: (i) μ = (1,1)T and Σ = 12 μ = 0 and Σ =…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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(i) μ = (1,1)T and Σ = 12 μ = 0 and Σ = 212 2 (iii) μ = 0 and 2 = (3 9) 0 -