WOLFRAM|DEMONSTRATIONS PROJECT

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.