In the second bullet point, what does it mean that "$X_1,X_2,...X_n$ are drawn from a common distribution"?
Does it simply mean they all have the same type of distribution (e.g. they are all normally distributed)?
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$\begingroup$ They are distributed from a common distribution, meaning they have the same density (rather than the same form of density). $\endgroup$– Xi'anCommented Dec 3, 2019 at 10:12
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2$\begingroup$ Not only same type of distribution, but also same parameter - i.e. not only are they all normally distributed, but with the same parameters $ \mu, \sigma^2 $ $\endgroup$– Itamar MushkinCommented Dec 3, 2019 at 10:49
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2$\begingroup$ The bullet points are redundant, making them confusing. You may safely erase 2, 3, and 4. $\endgroup$– whuber ♦Commented Dec 3, 2019 at 15:16
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1 Answer
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The entire five-bullet assumptions basically just mean that all $X_i$ are drawn from one distribution $N(\mu,\sigma^2)$, with some specific $\mu$ and $\sigma$ values; and that $X_i$ are independent one another. From @whuber in the comments, you can just use assumption 1 and 5 and still understand the same thing, since 2, 3, 4 are implications of assuming 5.
"Drawn from same distribution" means the two random values are drawn from one distribution, i.e. same distribution form (Normal) and same distribution parameter.
