the gamma distribution

logistic_guy

Full Member
Joined
Apr 17, 2024
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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?
 
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