Upper and lower probability inferences based on a sample from a finite univariate population

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Abstract
This paper provides detailed formulae for upper and lower probability inferences, based on a sample from a finite population with a discrete univariate observable characteristic, and directed towards the unknown parameters of the population or properties of a future sample. The model is set up in § 2 and the detailed formulae are given in § 3. Section 4 demonstrates a limited relationship with confidence statements and §5 explores some special cases.