An Illustration of the Central Limit Theorem Using Chi-Square Samples
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If is a random sample from a distribution with finite mean
and variance
, then the central limit theorem asserts that the density function of
approaches a standard normal density as
. If the underlying distribution is a
distribution with one degree of freedom, the density function of
can be derived exactly (see the details). This Demonstration compares that density (purple) with a standard normal density (blue) for various values of
.
Contributed by: Chris Boucher (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
If is a random sample from a
distribution with one degree of freedom and
, the density function of
is
.
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