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# Infinite Sequences of Random Variables and Their Convergence Properties

## Abstract

In a problem of statistical inference if we use a statistic Tn based on a random sample $X1,…,Xn$, then it is important to know how Tn behaves as the sample size $n→∞$. Various modes of convergence of Tn and tools for proving such convergences are developed in this chapter.

### Keywords

Modes of Convergence; Weak and Strong Laws of Large Numbers; Probability Inequalities.

## 3.1 Introduction

Let T be a statistic based on the data consisting of rv’s X1, …, Xn. Most statistical ...

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