Transformation of random variables

If X is a random variable described by the probability density f(x), and if Y=Y(X) then

File:Hepa img1079.gif

is the probability density of y. For a transformation of several random variables File:Hepa img1080.gif into File:Hepa img1081.gif one has

File:Hepa img1082.gif

where File:Hepa img1083.gif is the Jacobian or Jacobi Determinant of the transformation.

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