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Assume there's some normally distributed population ($X$) whose parameters ($\mu$, $\sigma$) are not known. A sample ($x_1$) of size $n$ is drawn from $X$, and statistics are calculated: $\bar{x}_1$ and $s_1$. Another sample, $x_2$ of size $m$, has yet to be drawn but will be.

I'd like use this information ($n$, $\bar{x}_1$, $s_1$, and $m$) to formulate closed-form expectations of $\bar{x}_2$ and $s_2$, and, after some research, it seems like posterior predictive distributions are the right tool here, specifically when paired with the Normal-gamma conjugate prior.

Could someone confirm this intuition and/or provide an example of using something like this?

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  • $\begingroup$ What do you mean by a sample of length m? Can you be more concrete? $\endgroup$ – activatedgeek Jun 24 at 21:27
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    $\begingroup$ @activatedgeek I should have said size instead of length. Does that clear it up? $\endgroup$ – cjken Jun 24 at 22:18

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