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Joint distribution function of z and |z|

  1. Jun 18, 2011 #1
    X and Y are 2 independent gaussian random variables with parameter a.
    Z = XY / (X-Y)
    W = XY / |X-Y|
    I am to find the joint distribution function of z and w.
    I know how to find pdf of Z but how could I use it to find the joint distribution function of z and w?
     
  2. jcsd
  3. Jun 19, 2011 #2
    Here Z and W have no joint pdf (because Z=+/-W) so you'll have to calculate the joint cdf directly. I'd suggest breaking it up into special cases, for example P[Z<=z,W<=w]=(1/2)P[Z<=z] if -z<=w<z.
     
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