- #1
spitz
- 60
- 0
Homework Statement
a) [itex]P(X=x)=pq^x,\,x\geq 0[/itex]
Find the PGF.
b) [itex]P(X=x)=pq^{|x|},\,x\,\epsilon\,\text{Z}[/itex]
Find the PGF.
2. The attempt at a solution
a) [itex]G_X(s)=E(s^X)=\displaystyle\sum_{x\geq 0}pq^x s^x=p\displaystyle\sum_{x\geq 0}(qs)^x=\frac{p}{1-qs}[/itex]
b) Not sure about this one... Is it: as above for [itex]x\geq0[/itex]. And for [itex]x<0[/itex]:
[itex]G_X(s)=E(s^X)=\displaystyle\sum_{x>0}pq^{-x} s^{-x}=p\displaystyle\sum_{x\geq 0}(qs)^{-x}=\ldots[/itex]
Last edited: