Derivation question

  • Thread starter roadworx
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  • #1
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Hi,

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] ?
 

Answers and Replies

  • #2
arildno
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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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