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If, we hAny from Lemma 2 that, with probability 1,.
Substituting (x_{L}=(x_{min}-mu /sigmaleq c_{L}<0) into the first inequality and (x_{min}-mu /sigmaleqigmageq c_{U}>0) into the second inequaL}<0, one gets the bounds x_{L}cdot sintoleq x_{i} -muleq x_{U}cdotheigma,quad i=1,ldots,n, (5.3) where (x_{L}leq c_{L}<0), (x_{U}geq c_{U}>0) are both solutions ofirst equatinequalityfrand1}{n}).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com