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Let U1 and U2 be iid Uniform[0,1]. Define X and Y by,
X =

 

2log(1/U1)
 
cos(2pU2),  Y =

 

2log(1/U1)
 
sin(2pU2)
Then the Jacobian |[((u1,u2))/((x,y))]| is,
  • 1
  • [1/(2p)]e-(x2+y2)/2
  • 2p
  • u1
  • [(u1)/(2p)]
  • *****
    calculator


    Carlos Rodriguez <carlos@math.albany.edu>
    This problem was contributed by a student. It is offered as it is with no warranty of any kind
    Last modified:Thu Sep 18 2008 15:09:49 GMT-0400 (Eastern Daylight Time)