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Central Limit Theorem for the Continuous Uniform Distribution

​
sample size n
1
This Demonstration illustrates the central limit theorem for the continuous uniform distribution on an interval. If
X
has the uniform distribution on the interval
[-1,1]
and
-
X
is the mean of an independent random sample of size
n
from this distribution, then the central limit theorem says that the corresponding standardized distribution
-
X
-μ
σ
-
X
approaches the standard normal distribution as
n∞
. Using operations on the characteristic function of
X
we can compute the PDF of
-
X
more easily than we could directly. The blue curve is the PDF of
-
X
-μ
σ
-
X
and the dashed curve is the PDF of a standard normal distribution.
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