# Chapter 4Expectation

## 4.1 Introduction

The distribution function or the density [pmf for a discrete random variable] completely characterizes the behavior of a random variable *X*. Frequently, however, we need a more concise description such as a single number or a few numbers, rather than an entire function. One such number is the **expectation** or the **mean**, denoted by . Similarly, the **median**, which is defined as any number *x* such that and , and the **mode**, defined as the number *x*, for which or attains its maximum, are two other quantities sometimes used to describe a random variable *X*. The mean, median, and mode are often called **measures of central tendency** of a random variable *X*.

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