How do you calculate experimental uncertainty using the Gaussian formula?

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SUMMARY

The Gaussian formula for calculating experimental uncertainty is accurately represented by the equation ΔN = sqrt [ ( (-a/y)*exp(-x/y)*Δx )² + ( (ax/y²)*exp(-x/y)*Δy )² ]. It is crucial to note that the variables y and x should be interchanged in the first term of the equation. This correction ensures the proper application of the Gaussian formula in uncertainty calculations.

PREREQUISITES
  • Understanding of Gaussian distribution and its applications
  • Familiarity with calculus, specifically derivatives
  • Knowledge of exponential functions and their properties
  • Basic grasp of experimental uncertainty concepts
NEXT STEPS
  • Study the derivation of the Gaussian formula for uncertainty calculations
  • Learn about the implications of variable interchanges in mathematical equations
  • Explore advanced topics in error propagation techniques
  • Investigate practical applications of Gaussian uncertainty in experimental physics
USEFUL FOR

Students in physics or engineering, researchers conducting experiments, and anyone involved in data analysis requiring precise uncertainty calculations.

raintrek
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erm the general idea is right but i guess your derivatives are wrong :)

you should get
ΔN = sqrt [ ( (-a/y)*exp(-x/y)*Δx )² + ( (ax/y²)*exp(-x/y)*Δy )² ]

y and x interchanged in first term :)

i hope that solves your problem otherwise i don´t know what´s wrong there the gauß formula is ok as far as i see :)
 

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