The discussion revolves around a random variable X characterized by its probability generating function gX(s) = (5-4s²)⁻¹. Participants are attempting to calculate specific probabilities, P(X=3) and P(X=4), using the properties of the generating function.
There is an ongoing exploration of the generating function's properties, with some participants providing calculations for g_X(0) and its derivative. However, there is no clear consensus on the implications of these calculations, and some confusion remains regarding the evaluation of the series at s=0.
Participants are navigating the constraints of the problem, including the need to derive probabilities from the generating function without explicit solutions being provided. There is uncertainty about the interpretation of the generating function's properties and their application to the problem at hand.
micromass said:What is [itex]g_X(0)[/itex]?? What is [itex]g^\prime_X(0)[/itex]?? (the derivative)
micromass said:Yes, and what if you calculate the same thing using
[tex]g_X(s)=\sum P\{X=k\}s^k[/tex]
??
tamintl said:Not sure what you mean but [tex]g_X(0)=\sum P\{X=3\}0^3[/tex]=0 ?
Sorry
micromass said:OK, if you have the series
[tex]P\{X=0\}+P\{X=1\}s+P\{X=2\}s^2+...[/tex]
what happens if I put s=0??
tamintl said:You will get '0'