I am having trouble approximating the sum of gamma-distributed variables via CLR.

I know via Gamma that $X=\sum_{i=1}^n X_i \\$ and $X\sim\Gamma(n\alpha,\beta) \\$

and $CLT: Z_{n}=\frac{\overline{X}-n\mu}{\sigma\sqrt{n}}$

Let's say n = 300, $X_i\sim\Gamma(0.6,0.3) \\$ so $X=\sum_{i=1}^n X_i \\$, $X\sim\Gamma(300*(0.6),0.3) \\$

$\mu = \frac{\alpha}{\beta} = 600.\\ \sigma^2 = \frac{\alpha}{\beta^2} = 2000\\ \sigma = 44.72\\$

For $Z_{n}$, does $n\mu$ refer to $300*\mu$?

Thanks in advance.

  • $\begingroup$ $n\mu$ is just $600$. $\endgroup$ – Kabo Murphy Mar 27 at 7:55

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