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 expected value. This appears to be inconsistent with conventional views of error estimation. The paradox is named for physicist R. T. Hodgson. If and are normal variables with arbitrary mean and variance, then has a Cauchy distribution, which has no first moment. 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). ==Reference== * R. T. Hodgson. "The problem of being a normal deviate", ''American Journal of Physics'' 47(12), December 1979.
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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 expected value. This appears to be inconsistent with conventional views of error estimation. The paradox is named for physicist R. T. Hodgson. If and are normal variables with arbitrary mean and variance, then has a Cauchy distribution, which has no first moment. 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). ==Reference== * R. T. Hodgson. "The problem of being a normal deviate", ''American Journal of Physics'' 47(12), December 1979.
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