Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sum of non-independent rv's

  1. Nov 2, 2012 #1
    f(x,y) = (1/x) for 0≤y≤x≤1

    A new rv Z=X+Y where X,Y not independent find the pdf of z

    My approach

    F(z) = P(Z≤z) = ∫∫fXY(x,y) dx dy x= -∞ to ∞ y= 0 to z-y

    f(z) = d/dz(F(z)) = ∫fXY(z-y,y) dy y= -∞ to ∞ (using Leibnitz)

    where i am stuck is this doesn't converge
  2. jcsd
  3. Nov 4, 2012 #2
    (this thread belongs in the homework forums)

    f(x,y) might not be a valid pdf
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook