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
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 Fall '08
 prellis
 Integrals, Probability

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