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Derivation question

  1. Apr 13, 2009 #1

    I have the following equation

    [tex]\gamma_0 = \phi^2 \gamma_0 + (1+\Theta^2)\sigma^2 + 2\Theta\phi\sigma^2[/tex]

    The answer is

    [tex]\gamma_0 = \frac{(1 + 2\Theta\phi+\Theta^2)}{1-\phi^2}[/tex]

    I get how to factorize the numerator. I'm not sure of the denominator. It looks like a geometric series formula, but does this mean [tex]\gamma_0[/tex] = [tex](1+\Theta^2)\sigma^2 + 2\Theta\phi\sigma^2[/tex] ?
  2. jcsd
  3. Apr 13, 2009 #2


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    1. A factor of sigma squared is lacking from the numerator.

    2. Subtract [itex]\phi^{2}\gamma_{0}[/itex] from both sides of the equation; factorize, and you'll see how the expression is arrived at.
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