- #1
juanma101285
- 5
- 0
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.
The solution says g(s)=1+s-s^2 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 g(s)=(1/3)*(1+s+s^4) and g(s)=(2-s^2)^{-1} are prob. gen. functions and that g(s)=1+s-s^2 and g(s)=(1/2)(1+s+s^3) 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.
The solution says g(s)=1+s-s^2 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 g(s)=(1/3)*(1+s+s^4) and g(s)=(2-s^2)^{-1} are prob. gen. functions and that g(s)=1+s-s^2 and g(s)=(1/2)(1+s+s^3) 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.
