Manipulating PGF for Probability Calculation

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SUMMARY

The discussion focuses on manipulating the probability generating function (PGF) Gx(s) = (4-s)/3(4-3s) to derive the probability mass function P(X=i) for a random variable X. The user, Jack, seeks guidance on eliminating the term (4-s) from the numerator to simplify the calculation. The solution involves multiplying out the (4-s) and applying the formula for the sum of an infinite geometric series, which allows for the extraction of P(X=i) without the s term remaining in the numerator.

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  • Knowledge of geometric series and their summation
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jackbauer
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Hi people, I was wondering if anyone could give me a hint with this problem.
A RV X has PGF Gx(s)= (4-s)/3(4-3s)

I need to get the P(X=i) from here. I know i can manipulate the above to get the sum to infinity of a geometric series, but i end up with the term
(4-s) still in the P(X=i) which i don't think can be right. Anybody got any hints on how to rearrange the above so as to eliminate the s in the numerator so I can obtain P(X=i)? Thanks a lot, Jack
 
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multiply out the (4-s) and the infinite series.
 

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