1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Attached Files:

  2. jcsd
  3. Apr 27, 2008 #2


    User Avatar
    Staff Emeritus
    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!!!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?