Mean, simplified from 3D to 1D

  • Thread starter pangyatou
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  • #1
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Hi,

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)

Thanks
 

Answers and Replies

  • #2
mathman
Science Advisor
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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.
 
  • #3
4
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Thanks Mathman!
What theory or property can be applied to this problem? I don't even have a clue.

Really appreciate.
 
  • #4
mathman
Science Advisor
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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.).
 
  • #5
Stephen Tashi
Science Advisor
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1,472
Hi,

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?
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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