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.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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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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