logistic_guy
Full Member
- Joined
- Apr 17, 2024
- Messages
- 288
here is the question
Show that the \(\displaystyle r\)th moment about the origin of the gamma distribution is \(\displaystyle \mu'_r = \frac{\beta^r\Gamma(\alpha + r)}{\Gamma(\alpha)}\).
my attemb
i think \(\displaystyle \alpha\) and \(\displaystyle \beta\) are the parameter of the gamma distribution
first moment
\(\displaystyle \mu'_1 = \frac{\beta^1\Gamma(\alpha + 1)}{\Gamma(\alpha)}\)
second moment
\(\displaystyle \mu'_2 = \frac{\beta^2\Gamma(\alpha + 2)}{\Gamma(\alpha)}\)
third moment
\(\displaystyle \mu'_3 = \frac{\beta^3\Gamma(\alpha + 3)}{\Gamma(\alpha)}\)
so i think there is infinite moments. do my proof correct?
Show that the \(\displaystyle r\)th moment about the origin of the gamma distribution is \(\displaystyle \mu'_r = \frac{\beta^r\Gamma(\alpha + r)}{\Gamma(\alpha)}\).
my attemb
i think \(\displaystyle \alpha\) and \(\displaystyle \beta\) are the parameter of the gamma distribution
first moment
\(\displaystyle \mu'_1 = \frac{\beta^1\Gamma(\alpha + 1)}{\Gamma(\alpha)}\)
second moment
\(\displaystyle \mu'_2 = \frac{\beta^2\Gamma(\alpha + 2)}{\Gamma(\alpha)}\)
third moment
\(\displaystyle \mu'_3 = \frac{\beta^3\Gamma(\alpha + 3)}{\Gamma(\alpha)}\)
so i think there is infinite moments. do my proof correct?