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Covariance between x and f(x)?

  1. May 7, 2012 #1
    1. The problem statement, all variables and given/known data
    As part of an assignment, I have to determine propagated error of some function:
    [itex]f(x,t)[/itex]
    I did it first with x & t being completely uncorrelated, but now I'm given x as a function of t, [itex]x(t)[/itex], and have to do the same.


    2. Relevant equations
    I know the linear approximation for finding the uncertainty [itex]\sigma_f[/itex], all I need is the covariance term.
    The equation x(t) itself is simply [itex]x(t) = a \sqrt{t}[/itex], where a is just a constant.

    3. The attempt at a solution
    I seem to be having a hell of a time Googling to find a way to calculate the covariance between t and x(t).
     
    Last edited: May 7, 2012
  2. jcsd
  3. May 8, 2012 #2

    I like Serena

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    Homework Helper

    Hi hb1547! :smile:

    I do not believe you need the covariance.
    Let's define g(t)=f(x(t),t).
    Then the uncertainty in g(t) is g'(t)σt.

    Do you know how to calculate g'(t)?
    It consists of a couple of partial derivatives and the chain rule...
     
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