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Since
is
positive
,
[3]. When the
probability density function
,
f(x)
, is graphed,
the area under the bell-shaped
, symmetric curve is one. See Figure 9. This can be proven using multi-variable calculus and incorporating polar
coordinates when integrating
[2].
In a normal distribution
,
it is also true that
and
.
In other words
,
and
are actually the mean and variance of the data sample. This is proven using the moment-generating functions of X [3].
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same amount
focus will be
actual value
simple case
is 
[3]. When the 
[2]. 
and 
. 
and 
are actually the mean and variance of the data sample. This is proven using the moment-generating functions of X [3].