The Point That Fights the Correlation

Samples (x,y) (x, y) are drawn from a bivariate Gaussian with mean at the origin and covariance matrix Σ=(1−0.5−0.51) \Sigma = \begin{pmatrix} 1 & -0.5 \\ -0.5 & 1 \end{pmatrix} . Among the four observations below, which one would you flag as the strongest outlier? I. (1,0) (1, 0) II. (1,−1) (1, -1) III. (−1,−1) (-1, -1) IV. (0,1) (0, 1)

Answer

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