Example 8:
X: the random variable
representing the flight time from
Suppose
the flight time can be any value in the interval from 30 to 50 minutes.
That
is, 
Question: if the probability of a
flight time within any time interval is the same as the one
within the other time
interval with the same length. Then, what density 
is
sensible for describing
the probability?
Recall
that the area under the graph of corresponding to
any interval is the probability
of
the random variable X taking values in this interval. Since the probabilities
of X taking
values
in any equal length interval are the same, then the the areas under the graph
of
corresponding
to any equal length interval are the same. Thus,
will take the
same
value
over any equal length area. For example, within
one minute interval, then
Therefore,
we have
Note: since we know 
, then by the property that
.
In
the above example, the probability density has the same value in the interval
the random
variable
taking value. This probability density is referred as the
uniform probability density function.
Uniform Probability Density Function:
A
random variable X taking values in [a,b] has the uniform probability density
function
if
.
Properties of Uniform Probability Density Function:
A
random variable X taking values in [a,b] has the uniform probability density
function ,
then
Example 8 (continue):
In the
flight time example, 
then
JavaStatSoft:
Probability
density:
Statistics
-> Probability -> Probability Functions -> Probability Density
Function (PDF)
Probability
density:
Statistics
-> Probability -> Probability Functions -> Cumulative Distribution
Function (CDF)
Percentile
(or Quantile):
Statistics
-> Probability -> Probability Functions -> Percentile Function