Exercise 12.9.7. Let y be an observation from one of two normal populations that have means of
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Exercise 12.9.7. Let y be an observation from one of two normal populations that have means of μ1 and μ2 and common covariance matrix Σ . Define λ = (μ1−
μ2)Σ −1.
(a) Show that, under linear discrimination, y is allocated to population 1 if and only if
λ y−λ 1 2
(μ1+μ2) > 0.
(b) Show that if y is from population 1, E(λ y)−λ 1 2
(μ1+μ2) > 0 and if y is from population 2, E(λ y)−λ 1 2
(μ1+μ2) < 0.
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