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Probability distribution function with arctan

  1. Dec 15, 2008 #1
    Hi I have a function [tex]\phi =arctan(Y/X)[/tex] where, X[tex]\sim \mathcal{N}(A\cos \theta, v)[/tex] and Y[tex]\sim \mathcal{N}(A\sin \theta,v)[/tex]. I want to find
    pdf (probability distribution) of [tex]\phi [/tex]. Any suggestions ? I think change of variables in integral might work??
  2. jcsd
  3. Dec 16, 2008 #2
    There's a change of variables formula for two r.v.s for situations like this. It amounts to changing variables in the integral of the joint pdf.
  4. Dec 17, 2008 #3
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