Mean and minimum of independent random variables
نویسندگان
چکیده
We show that any pair X, Y of independent non-compactly supported random variables on [0, ∞) satisfies $$\mathop {\lim \inf}\limits_{m \to \infty} \mathbb{P}(\min (X,Y) > m\,\left| {X + 2m} \right.) = 0.$$ .We conjecture multi-variate and weighted generalizations this result, prove them under the additional assumption are identically distributed.
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2021
ISSN: ['1565-8511', '0021-2172']
DOI: https://doi.org/10.1007/s11856-021-2195-0