Abstract
Probability distribution functions and lowest statistical moments of composite measurements representable as products and quotients of independent normal variates are derived, and tested by means of the α and β branching decays of 212Bi. The exact composite distribution functions are non-Gaussian and provide correct uncertainty estimates and confidence intervals in cases where standard error propagation relations are inaccurate. Although nuclear decay processes give rise to Poisson-distributed parent populations, the Gaussian-based composite distributions form nearly perfect envelopes to the discrete distributions of products and ratios of Poisson variates, even for relatively low counts. To our knowledge, this is the first reported experimental test of the statistics of composite measurements by a fundamental quantum process.