Hi, I have a problem that is already solved... I thought 3 of the 4 functions were probability generating functions, but I got one wrong and don't know why.(adsbygoogle = window.adsbygoogle || []).push({});

The solution says [itex]g(s)=1+s-s^2[/itex] is not a probability generating function. However, g(1)=1 and I think g(s) converges to 1 for |s|<1. Isn't that correct? If so, what is it that invalidates this function as a probability generating function?

The solution says that [itex]g(s)=(1/3)*(1+s+s^4)[/itex] and [itex]g(s)=(2-s^2)^{-1}[/itex] are prob. gen. functions and that [itex]g(s)=1+s-s^2[/itex] and [itex]g(s)=(1/2)(1+s+s^3)[/itex] are not (I know the last one is not because g(1)=3/2).

Thanks a lot for your help! :) And if you could also give me an explanation of other things I need to look for in a function to tell if it is a p.g.f., I would really appreciate that.

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Cannot tell when a probability generating function converges for |s|<1

Loading...

Similar Threads - Cannot tell probability | Date |
---|---|

Impossible to make a program to tell whether a program runs forever | Aug 28, 2014 |

A proof that a computer cannot generate a truly random number? | May 11, 2013 |

Kolmogorov smirnov in r - cannot compute correct p-values with ties | Jan 18, 2013 |

Are there things language cannot describe? | Jan 19, 2012 |

Hypothesis testing, why alpha cannot be zero | Jul 24, 2011 |

**Physics Forums - The Fusion of Science and Community**