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Old 12-11-2018, 02:43 AM
imrancairo imrancairo is offline
 
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Post Transformation of Jointly Dist. R.V

Consider the transformation: Y1=X1−X2, Y2=X1+X2. We wish to find the joint distribution of Y1 and Y2.

We have

x1=y1+y2/2, x2=y2−y1/2 OR v1(y1,y2)=y1+y2/2,v2(y1,y2)=y2−y1/2


i cant understand how y1+y2/2 and y2-y1/2 derived??

Pls. help me best regard to all
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Old 12-11-2018, 09:29 AM
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Gandalf Gandalf is offline
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It is just regular algebra, solving 2 linear equations in 2 unknowns. For the first, just add the two equations (add left sides and right sides).

Y1=X1−X2
Y2=X1+X2

Y1+Y2 = 2 X1

X1 = (Y1+Y2)/2

(The way you wrote it was confusing without parentheses, but the picture clearly shows Y1 and Y2 each divided by 2.)

Similarly for X2; subtract the equations.
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Old 12-12-2018, 12:56 AM
imrancairo imrancairo is offline
 
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Thanks Sir!
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