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Easy problem

  1. Apr 27, 2008 #1
    can someone explain to me how did it derived to the ARROW...
    I am not quite sure how that happened.thanks
     

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  2. jcsd
  3. Apr 27, 2008 #2

    HallsofIvy

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    Science Advisor

    You have
    [tex]e^{-\frac{x^2+ y^2- 2\rho xy}{2\sigma(1-\rho)^2}}[/itex]
    They complete the square:
    [tex]x^2- 2\rho xy+ \rho^2y^2- \rho^2y^2+ y^2= (x- \rho y)^2+ (y^2- \rho^2 y^2)[/tex]
    so the exponential becomes
    [tex]e^{-\frac{(x-\rho y)^2- (y^2- \rho^2 y^2)}{2\sigma(1-\rho)^2}}[/itex]
    Then separate the exponentials:
    [tex]e^{-\frac{(x- \rho y)^2}{2\sigma(1-\rho)^2}}e^{-\frac{(y^2- \rho^2 y^2}{2\sigma(1-\rho)^2}}[/tex]
    and finally factor out y2 in the last exponential
    [tex]e^{-\frac{(x- \rho y)^2}{2\sigma(1-\rho)^2}}e^{-\frac{y^2(1- \rho^2}{2\sigma(1-\rho)^2}}[/tex]
     
  4. Apr 27, 2008 #3
    Thank You So Much!!!
     
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