Probability
In this last application of integrals that we’ll be looking at we’re going to look at probability.
Before actually getting into the applications we need to get a couple of definitions out of the way.
Suppose that we wanted to look at the age of a person, the height of a person, the amount of time
spent waiting in line, or maybe the lifetime of a battery. Each of these quantities have values that
will range over an interval of integers. Because of this these are called
continuous random
variables
. Continuous random variables are often represented by
X
.
Every continuous random variable,
X
, has a
probability density function
,
.
Probability density functions satisfy the following conditions.
1.
for all
x
.
2.
Probability density functions can be used to determine the probability that a continuous random
variable lies between two values, say
a
and
b
. This probability is denoted
by
and is given by,
Let’s take a look at an example of this.
Example 1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 prellis
 Integrals, Probability, Probability theory, probability density function, 10 minutes, 6 minutes, 6 minutes, 8.658%

Click to edit the document details