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