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Mean, simplified from 3D to 1D

  1. Nov 1, 2011 #1

    There are three variables ax, ay and az, my question is:
    How to simplify the mean value <(ax^2+ay^2+az^2)^(1/2)> to <|ax|> ?
    What assumptions are required during the simplification?

    The statistical property of ax, ay and az is <ax^2>=<ay^2>=<az^2>.
    The assumption of the propability is: pdf(ax), pdf(ay) and pdf(az) are independent to each other: p(ax,ay,az)=p(ax)p(ay)p(az)

  2. jcsd
  3. Nov 1, 2011 #2


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    No further assumptions are needed to carry out the calculation. It is messy because you are taking the square root before calculating the integral.
  4. Nov 1, 2011 #3
    Thanks Mathman!
    What theory or property can be applied to this problem? I don't even have a clue.

    Really appreciate.
  5. Nov 2, 2011 #4


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    It is a 3-d integral where the integrand is the product of the 3 density functions multiplied by the expression (square root etc.).
  6. Nov 2, 2011 #5

    Stephen Tashi

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    Are you asking if the mean value of [itex] r = \sqrt{a_x^2 + a_y^2 + a_z^2} [/itex] must be equal to the mean value of the absolute value of [itex] a_x [/itex] ?
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