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I have a physical quantity A defined as $A=(74.5 B^2*(M+N))^{1/3}$

where B, M, N and relative uncertainties are given. And M and N are dependent on B:

$log M=(0.755 \pm 0.059)*log B+(0.416\pm 0.024)$

$log N=(0.352 \pm 0.166)*log B-(0.262\pm 0.067)$

This two relations are the results of fitting a lot of data and it is assumed that the error on M, N is 15%.

The value of B is given by a software, and it is known with uncertainty 0.0002.

I need to know how this uncertainties affect the value of A. Can I use the fomula reported in the paragraph "Simplification" in the wikipedia page?

sunrise
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1 Answers1

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ANSWER 1

You're asking about error propagation. In your case:

$\sigma_{M+N} = \sqrt{\sigma_M^2 + \sigma_N^2}$

$3\dfrac{\sigma_A}{A} = \sqrt{2(\dfrac{\sigma_B}{b})^2 + (\dfrac{\sigma_{M+N}}{M+N})^2} $

The wrinkle in my calculation is that I assume that the errors in B, M and N are independent. Since M and N are functions of B that isn't strictly true.

(I asked in a comment on the question for more information on B - don't know if that information will be shared or not.)

ANSWER 2

You could calculate the error experimentally. Generate the appropriate random errors for each value assuming the normal distribution and calculate values for A 1000 times. Then calculate the mean and std dev of A.

Gaussian errors are calculated by using a random number between 0 and 1, then using the CDF of the normal distribution to do a reverse lookup of the std dev.

MaxW
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