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Box-Muller transform

  1. Feb 3, 2016 #1
    In derivation of the box-muller transform, the joint distribution p(x,y) = e^(-r^2/2)/(2*pi) is interpreted as the product of a uniform distribution 1/(2*pi) and an exponential distribution e^(-x/2), but isn't an exponential distribution defined as k*e^(-k*x)? What happened to the coefficient?
     
  2. jcsd
  3. Feb 3, 2016 #2

    mathman

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    You are missing a constant.
     
  4. Feb 3, 2016 #3

    mathman

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    derivation: Start with [itex]\frac{1}{2\pi}e^{\frac{-x^2-y^2}{2}}dxdy[/itex]. Change to polar coordinates. [itex]\frac{1}{2\pi}e^{\frac{-r^2}{2}}
    rdrd\theta[/itex]. For you picture [itex]s=r^2,\ so\ ds=2rdr,\ or\ rdr=\frac{ds}{2}[/itex]. There's the coefficient.
     
  5. Feb 4, 2016 #4
    Thanks mathman :)
     
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