Chapter 4Expectation

4.1 Introduction

The distribution function c04-math-0001 or the density c04-math-0002 [pmf c04-math-0003 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 c04-math-0005. Similarly, the median, which is defined as any number x such that c04-math-0007 and c04-math-0008, and the mode, defined as the number x, for which c04-math-0010 or c04-math-0011 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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