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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