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On an example of expectation evaluation
Teoriâ veroâtnostej i ee primeneniâ, Tome 69 (2024) no. 2, pp. 393-404 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the distribution of the maximal element $\overline{\xi}_n$ of a sequence of (possibly) independent random variables $\xi_1,\dots,\xi_n$. A formula for evaluation of a random variable expectation based on a quantile function is considered. This formula is applied to evaluation of the expectation for a nondecreasing function of a random variable transformed via its distribution function. The case of a discontinuous distribution function is the most interesting. As a corollary, we refine an example proposed in the author's previous article [Theory Probab. Appl., 68 (2023), pp. 392–410].
Keywords: expectation, quantile function, transformation of a variable using its distribution function, application to statistical estimates of mutual information. 
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Al. V. Bulinski. On an example of expectation evaluation. Teoriâ veroâtnostej i ee primeneniâ, Tome 69 (2024) no. 2, pp. 393-404. http://geodesic.mathdoc.fr/item/TVP_2024_69_2_a10/

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