PGF of Discrete Random Variable

**sirellwood** · March 12th 2010, 08:32 AM

Hi Everyone,

I am trying to show that the discrete random variable....

P(R=j) = $(j+1)$ $p^j$ ${(1-p)}^2$ , j = 0,1,2,.... 0<p<1

Has a P.G.F.....

GR(s) = ( $\frac{1-p}{1-ps}$ )^2

Above is meant to be the whole fraction to the power 2, but i was having some Latex Syntax problems showing that

I have tried changing $s^j$ and $p^j$ to $ps^j$ and taking it outside the summation when beginning to try and find the PGF but i didnt get anywhere, help needed please!

Also maybe $\Sigma$ $(j+1)$ $a^j$ ${(1-a)}^2$ = 1 for any a where $\mid$ a $\mid$ < 1 can be used? i cant see how though!

**matheagle** · March 12th 2010, 02:17 PM

you placed the math OUTSIDE the [tex] tex [ /math]

Originally Posted by sirellwood

Hi Everyone,

I am trying to show that the discrete random variable....

P(R=j) = $(j+1)$ $p^j(1-p)^2$ , j = 0,1,2,.... 0<p<1

Has a P.G.F.....

GR(s) = $\left(\frac{1-p}{1-ps}\right)^2$

Above is meant to be the whole fraction to the power 2, but i was having some Latex Syntax problems showing that

I have tried changing $s^j$ and $p^j$ to $ps^j$ and taking it outside the summation when beginning to try and find the PGF but i didnt get anywhere, help needed please!

Also maybe $\Sigma$ $(j+1)$ $a^j$ ${(1-a)}^2$ = 1 for any a where $\mid$ a $\mid$ < 1 can be used? i cant see how though!

The trick in these is to differentiate the geometric, that brings downs that power of j.

Inside the interval of convergence you can..........

${d\over dx} \sum_{n=0}^{\infty}x^n=\sum_{n=1}^{\infty}nx^{n-1}$

**sirellwood** · March 12th 2010, 02:22 PM

Thanks matheagle! any ideas on how to solve the question? :-)

**sirellwood** · March 12th 2010, 04:21 PM

Sorry matheagle, first time id loaded your post, the extra bit at the bottom hadnt loaded! :-)

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