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Uncorrelated uncertainties

  1. Jan 29, 2009 #1
    1. The problem statement, all variables and given/known data
    For uncorrelated uncertainties LaTeX Code: \\delta x and LaTeX Code: \\delta y give the values and uncertainties for W in standard format.
    A.) W=x+y with x=4.2(0.2) and y=0.7(0.1)

    2. Relevant equations



    3. The attempt at a solution
    well i think i am supposed to take the partial derivatives of W with respect to x and y (dW/dx and dW/dy) which both =1. Then is the total derivative DW/DXorY = 1+1 dx/dy? Or do I only use the derivatives for the uncertainties and just plug x and y, 4.2 and 0.7, into W?
     
  2. jcsd
  3. Jan 30, 2009 #2

    CompuChip

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    If you have a function [itex]f(x_1, x_2, \cdots, x_n)[/itex] where all the variables [itex]x_i[/itex] have their own uncertainty [itex]\Delta x_i[/itex], then what is the central value for f?
    For the uncertainty there is a formula which involves the partial derivatives, but it's not what you seem to think it is. IIRC it is
    [tex](\Delta f)^2 = \sum_{i = 1}^n \left( \frac{\partial f}{\partial x_i} \Delta x_i \right)^2[/tex]
    but you can probably look that up in your textbook.
     
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