1.3 Population and Sample
Definition 1.4. A random sample of size \(n\) from a distribution is a sequence \(X_1, \ldots , X_n\) of independent observations, each having that distribution.
Independence means that knowing one value tells us nothing about the others. It is the requirement most often violated in practice and the one whose violation does most damage — Chapter 6 returns to exactly this point for time-ordered data.
In practice we rarely sample from a cleanly specified distribution. If a new diet is tested on twenty pigs at one agricultural station, the twenty are not a random sample from all pigs; they are the pigs available. The population being sampled is then a hypothetical one, and the inference is only as good as that idealisation.
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