Thread: moment generating function question

1. moment generating function question

find the moment generating function of f(x)= 2^(-x) , x= 1,2,3,....

2. Originally Posted by omoboye
find the moment generating function of f(x)= 2^(-x) , x= 1,2,3,....
$M_X(t)=E(e^{tx})$

.......... $\displaystyle = \sum_{x=1}^{\infty}e^{tx}2^{-x}=\sum_{x=1}^{\infty}e^{tx}e^{-x\ln(2)}$

which for $t<\ln(2)$ is a convergent geometric series.

CB