Hi Everyone,

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

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

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

G

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

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

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