Random means generated by random variables: expectation and limit theorems

TL;DR

This paper introduces the concept of random means generated by random variables, providing a framework for their expectation and establishing limit theorems including strong laws of large numbers for sequences of i.i.d. random variables.

Contribution

It presents a novel definition of random means and derives conditions under which classical limit theorems apply to these means.

Findings

Defined random means generated by random variables

Established conditions for strong laws of large numbers for random means

Proved limit theorems for sequences of i.i.d. random variables

Abstract

We introduce the notion of a random mean generated by a random variable and give a construction of its expected value. We derive some sufficient conditions under which strong laws of large numbers and some limit theorems hold for random means generated by the elements of a sequence of independent and identically distributed random variables.