Hodgson's paradox

In statistics and physics, Hodgson's paradox is the observation that the ratio of two Normally distributed random variables has neither mean nor variance, and thus no well-defined expectation. This appears to be inconsistent with conventional views of error estimation. The paradox is named for physicist R. T. Hodgson.

Related Topics:
Statistics - Physics - Normal - Random variables - Mean - Variance - Expectation - R. T. Hodgson

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If X and Y are normal variables with arbitrary mean and variance, then X/Y has a Cauchy distribution, which has no first moment.

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The resolution of the paradox is to observe that random variables are never exactly Gaussian. The example Hodgson uses is that of the height of men: this cannot be Gaussian because heights cannot be negative (and the PDF for the normal distribution is positive for the whole real line).

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