**Definition
2..1**

Suppose is a set with typical element , and let be a subset of . The indicator function of , denoted by , is defined by

(2.1) |

That is, __indicates__ the set . Some
properties of the indicator function are listed.

- (a)
- where is the complement of .
- (b)
- (c)
- (d)
- (e)

The following example shows a use for indicator functions.

**Example
2..1**

Suppose random variable has pdf given by

We can write as

or more concisely

Bob Murison 2000-10-31