GATE 2020 ST – Question 43
Two bivariate-normal populations have means(0,0),(1,1), common covariance $\begin{pmatrix}1&.5\\.5&1\end{pmatrix}$, equal priors and equal misclassification costs. For z₁=(.75,.75),z₂=(.25,.25), apply the linear discriminant rule.
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Correct answer: (B) z₁→P₂,z₂→P₁
Explanation
With common covariance and equal priors, compare Mahalanobis distances or the linear discriminant difference. Symmetry puts the boundary at z₁coordinate+z₂coordinate=1. The point(.75,.75) has sum1.5 and is nearer mean(1,1);(.25,.25) has sum0.5 and is nearer(0,0). Thus B.