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When talking about random variables, are the words deviate, variate, draw, realization all proper terminology and equivalent to each other?

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I would say these are mostly synonyms. There might be some weak shades of meaning, like "draw" mostly used in the context of simulation.

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    $\begingroup$ "Deviate" carries a sense of being measured relative to a mean, most commonly of a normal or Gaussian distribution. $\endgroup$
    – Nick Cox
    Commented Sep 5, 2017 at 14:55

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