calculate mahalanobis distance between two populations when the common dispersion matrix =25.05.01and the means are t)0.0,0.0(1=and t)0.1,0.1(2=where t denotes transpose.
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D1^2 = (x−μ1)T S1^−1 (x−μ1)
D2^2 = (x−μ2)T S2^−1 (x−μ2)
D3^2 = (x−μ3)T S3^−1 (x−μ3)
NF (Normalization Factor) = e^(-D1^2)+e^(-D2^2)+e^(-D3^2)
P1 (Probability of belonging to collection 1) = e^(-D1^2)/NF
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