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Propagation of uncertainty. In statistics, propagation of uncertainty (or propagation of error) is the effect of variables ' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have uncertainties due to measurement ...
v. t. e. Canonical commutation rule for position q and momentum p variables of a particle, 1927. pq − qp = h / (2 πi). Uncertainty principle of Heisenberg, 1927. The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with ...
Experimental uncertainty analysis. Experimental uncertainty analysis is a technique that analyses a derived quantity, based on the uncertainties in the experimentally measured quantities that are used in some form of mathematical relationship ("model") to calculate that derived quantity. The model used to convert the measurements into the ...
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This approximate formula is for moderate to large sample sizes; the reference gives the exact formulas for any sample size, and can be applied to heavily autocorrelated time series like Wall Street stock quotes. Moreover, this formula works for positive and negative ρ alike. [12] See also unbiased estimation of standard deviation for more ...
It is remarkable that the sum of squares of the residuals and the sample mean can be shown to be independent of each other, using, e.g. Basu's theorem.That fact, and the normal and chi-squared distributions given above form the basis of calculations involving the t-statistic:
Measurement uncertainty. In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a quantity measured on an interval or ratio scale. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty ...
When designing an organ or Boomwhacker, the diameter of the tube must be taken into account. In acoustics, end correction is a short distance applied or added to the actual length of a resonance pipe, in order to calculate the precise resonant frequency of the pipe. The pitch of a real tube is lower than the pitch predicted by the simple theory.