Random Sample

Topics: Statistics

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(definition)

A random sample is a collection of random variables $X_1,\dots ,X_n$ that satisfy the condition of being independent and having all the same distribution (i.e. they’re iid).

Random samples are used to formalise the concept of sampling a phenomenon whose behaviour is dictated by a random variable. Observing (i.e. obtaining realisations) a random variable $X$ $n$ times is equivalent to observing the random sample $X_1,\dots ,X_n$ just once.