Question

6. Suppose that fish come in two classes, salmon (class 1) and sea bass (class 2). We take a picture of a fish and measure its length, x, and wish to make a decision on the identity of the fish based on the value of x. Determine the decision regions in x for the Bayes classifier corresponding to the two classes under the following conditions (a) We assume that the class conditional densities are Gaussian with the following means, variances and class prior probabilities m 30,o 15,m 45,o,-15 p(salmon) 0.5, p(sea bass) 0.5 (b) We assume that the class conditional densities are Gaussian with the same parameters in (a), but the class prior probabilities are changed to p(salmon)- 0.9, p(sea bass) 0.1 (c) We assume that the class probabilities are the same as in (a), but that the conditional densities are Gaussian with the following means, variances and class prior probabilities m 30,o1 30,m2 45,o215, Note that the variances of the two classes in this part are different.

Answer 1

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c) chowe class: - 30) /0 Ln χ-30

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