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Given a set of three states of nature = {w₁,w2, w3} with prior probabilities P(w₁) = 0.2, P(₂)=0.3 and P(w3) = 0.5. In addition, each observation is

Given a set of three states of nature = {w₁,w2, w3} with prior probabilities P(w₁) = 0.2, P(₂)=0.3 and P(w3) = 0.5. In addition, each observation is

Calculus For The Life Sciences
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.
Chapter12: Probability
Section12.EA: Extended Application Medical Diagnosis
Problem 3EA
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represented by a scalar x with Gaussian class-conditional probability density functions (pdf) p(x | w₁) ~ N(14₁ 07) (1 ≤ i ≤3). Specifically, we have 141= -1, 112=0, s=2 and 1=2, 02=1, 03 = 3. Please answer the following questions: a) In case of minimum-error-rate classification, which state of nature should we decide for x-1.5? b) Suppose we have a set of two possible actions A= (a₁, a2) with the following loss function: Action Class α = α1 α = α₂ w = wi 5 10 w=6₂ 10 30 ولنا = لا 20 3 For an observation x with value 0.5, which action should we apply on x?
Transcribed Image Text:represented by a scalar x with Gaussian class-conditional probability density functions (pdf) p(x | w₁) ~ N(14₁ 07) (1 ≤ i ≤3). Specifically, we have 141= -1, 112=0, s=2 and 1=2, 02=1, 03 = 3. Please answer the following questions: a) In case of minimum-error-rate classification, which state of nature should we decide for x-1.5? b) Suppose we have a set of two possible actions A= (a₁, a2) with the following loss function: Action Class α = α1 α = α₂ w = wi 5 10 w=6₂ 10 30 ولنا = لا 20 3 For an observation x with value 0.5, which action should we apply on x?
Given a set of three states of nature = {w₁,w2, w3} with prior probabilities P(w₁) = 0.2, P(w₂) = 0.3 and P(3) = 0.5. In addition, each observation is
Transcribed Image Text:Given a set of three states of nature = {w₁,w2, w3} with prior probabilities P(w₁) = 0.2, P(w₂) = 0.3 and P(3) = 0.5. In addition, each observation is
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