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Sum of two random variables

  1. Mar 28, 2010 #1
    Hi,

    I've been working on this problem but I feel like I'm over complicating it. If you have a random variable X= a*e(j*phi), where phi is uniform on the interval [0,2pi) and a is some constant, and another random variable Y= b where b is a constant. I'm looking to find the probability density function of the random variable Z=X+Y.

    This is probably really simple but from what Ive been trying to do, I can just take the fourier transform of X, fourier transform of Y multiply them, and then take the inverse fourier of that, but it doesn't seem to work. How can I do this?
     
  2. jcsd
  3. Mar 29, 2010 #2

    mathman

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    You haven't defined j. If I can assume you mean i (sqrt(-1)), then X (complex variable) is uniformly distributed on a circle of radius a, centered at 0. Z is then uniformly distributed on a circle of radius a centered at b.
     
  4. Mar 29, 2010 #3
    yes, i apologize, j is sqrt(-1). After defining in matlab phi=rand(1,M).*2*pi where M=1000, i plotted Z= b+a.*exp(j.*phi) for various values of a and b and it looked kinda like an upside gaussian distribution centered about pi. Is this right?
     
  5. Mar 29, 2010 #4
    *upside down gaussian distribution
     
  6. Mar 30, 2010 #5

    mathman

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    I'm confused about what you did, since Z is complex, not real.
     
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