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Unformatted text preview: ∂x 1 ∂y 1 = cos y 2 , ∂x 1 ∂y 2 =y 1 sin y 2 , ∂x 2 ∂y 1 = sin y 2 , ∂x 2 ∂y 2 = y 1 cos y 2 . Therefore, the Jacobian is given by J = ± ± ± ± ± ± ± ∂x 1 ∂y 1 ∂x 1 ∂y 2 ∂x 2 ∂y 1 ∂x 2 ∂y 2 ± ± ± ± ± ± ± = ± ± ± ± cos y 2y 1 sin y 2 sin y 2 y 1 cos y 2 ± ± ± ± = y 1 cos 2 y 2 + y 1 sin 2 y 2 = y 1 . Thus, using the traditional notation, J = r . i.e., d x d y = r d r d θ ....
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This note was uploaded on 03/26/2012 for the course STAT 351 taught by Professor Michaelkozdron during the Fall '08 term at University of Regina.
 Fall '08
 MichaelKozdron
 Statistics, Probability

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