If the two random variables are uncorrelated, $3\sigma$ limit would mean that the random variables lie inside a hyperrectangle with center coordinates being means of random variables. But if two random variables are correlated, is taking a hyperrectangle instead of corresponding hyperellipsoid an under-approximation or altogether not theoretically correct?
2026-03-25 01:16:51.1774401411
Is taking $3\sigma$ limits for bivariate correlated random variables as the confidence limits an under estimation?
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