Summary
It is shown that a normal probability density can be characterized as a limit of conditional probability densities of i.i.d. uniform random variables.
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Choi, B.S. A conditional limit construction of the normal probability density. Ann Inst Stat Math 37, 535–539 (1985). https://doi.org/10.1007/BF02481122
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DOI: https://doi.org/10.1007/BF02481122