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MathGroup Archive 2009

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Distributing square-root (1/2) power through exponential equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg101296] Distributing square-root (1/2) power through exponential equation
  • From: Steven Matthew Anderson <AdAstra69 at mac.com>
  • Date: Tue, 30 Jun 2009 06:35:02 -0400 (EDT)

I'm playing with normal distributions, Two random points 1 and 2 with x and y coordinates given by:

px1=PDF[NormalDistribution[Mu,Sx],X1]
px2=PDF[NormalDistribution[Mu,Sx],X1]
py1=PDF[NormalDistribution[Mu,Sy],Y1]
py2=PDF[NormalDistribution[Mu,Sy],Y2]

The square of the Euclidean Distance between them is

SqD = (px2-px1)^2+(py2-py1)^2

Take the square root and expand of that to get

Dist = Sqrt[Expand[SqD]]

Now the question:  

How do I get the square root to act just like another power so I can simplify this mess?  I have tried PowerExpand, FullSimplify, Expand, Simplify, and various combinations.  Not sure what I'm missing here.


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