This article is devoted to establish the distributions for Sombor indices in a general random chain, in which their explicit analytical expressions of the expected values and variances are obtained. As applications, these results for random hexagonal, random phenylene, random polyphenyl and random spiro chains are given. Finally, the distributions for the Sombor indices in these four random chains are asymptotic to normal distributions is shown.

中文翻译：

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一般随机链中 Sombor 指数的期望值和方差

本文致力于建立一般随机链中 Sombor 指数的分布，其中获得了它们的期望值和方差的显式解析表达式。作为应用，给出了无规六方链、无规亚苯基、无规多苯基和无规螺链的这些结果。最后，显示了这四个随机链中 Sombor 指数的分布渐近于正态分布。