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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