Problem 58941. Compute measurement uncertainty
Suppose a variable y depends on n independent variables , , . If the independent variables have uncertainty , , etc. and the uncertainties are independent, then the uncertainty in y can be estimated with
For this problem, the relationship between y and will be power laws of the form
For example, the relationship would have c = 0.5 and a = [1 2].
Write a function that takes a vector of values of x, the coefficient c, exponents a, and a vector of uncertainties and returns the absolute uncertainty , relative uncertainty , and the index of the variable that contributes the most to the uncertainty in y. Identifying the largest contributor to the uncertainty tells the experimentalist which measurement to target first to improve the measurement.
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