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4. Two populations with known pdf's, that is, ₁, i = 1,2 has SN (₁, 0², a), where X~ SN (μ, o², a) if its density is given by 2 χ-μ x-μ f(x) = = ²/ 6 ( ² − ¹) + ( a ² −¹ ), -0 Φ σ σ x = R₁ μ € R, and o> 0. (.) and (.) are the pdf (probability density function) and cdf (cumulative distribution function) of standard normal dis- tribution. a. Find a classification rule, which minimize the ECM (Expected Cost of Misclassification) when cost and prior ratios are equal. b. The classification function found in a. is a linear function? c. What happens if a = 0? Find the classification function using a = 0.

4. Two populations with known pdf's, that is, ₁, i = 1,2 has SN (₁, 0², a), where X~ SN (μ, o², a) if its density is given by 2 χ-μ x-μ f(x) = = ²/ 6 ( ² − ¹) + ( a ² −¹ ), -0 Φ σ σ x = R₁ μ € R, and o> 0. (.) and (.) are the pdf (probability density function) and cdf (cumulative distribution function) of standard normal dis- tribution. a. Find a classification rule, which minimize the ECM (Expected Cost of Misclassification) when cost and prior ratios are equal. b. The classification function found in a. is a linear function? c. What happens if a = 0? Find the classification function using a = 0.

MATLAB: An Introduction with Applications
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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4. Two populations with known pdf's, that is, T;, i = 1,2 has SN(Hi, o?, a), where X SN(u, o?, a) if its density is given by f(x) = Ф x € R, µ E R, and o > 0. 0() and (-) are the pdf (probability density function) and cdf (cumulative distribution function) of standard normal dis- tribution. a. Find a classification rule, which minimize the ECM (Expected Cost of Misclassification) when cost and prior ratios are equal. b. The classification function found in a. is a linear function? c. What happens if a = 0? Find the classification function using a = 0.
Transcribed Image Text:4. Two populations with known pdf's, that is, T;, i = 1,2 has SN(Hi, o?, a), where X SN(u, o?, a) if its density is given by f(x) = Ф x € R, µ E R, and o > 0. 0() and (-) are the pdf (probability density function) and cdf (cumulative distribution function) of standard normal dis- tribution. a. Find a classification rule, which minimize the ECM (Expected Cost of Misclassification) when cost and prior ratios are equal. b. The classification function found in a. is a linear function? c. What happens if a = 0? Find the classification function using a = 0.
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