Notation for assigning observations to a random variable

notationrandom variablesstatistics

I want to assign some observations to a variable $X$, but I am unsure what the correct notation (if any) would be. At the moment I am doing it like this:

For the following set of observations for X,
$$1,8,1,5,8,6,3,3,3,7$$
…

But I was wondering if there was any actual notation where I could write something like this:

For the following set of observations
$$X = \{1,8,1,5,8,6,3,3,3,7\}$$
…

I dont think the latter is correct, since the random variable $X$ is not actually a set, but I wanted to know if there was any sort of similar notation to indicate the values observed for $X$.

Best Answer

Blitzstein considers in his book the 5x flipping a coin and writes:

  • The random variable $X = \{\{x_1, x_2, x_3, x_4, x_5\}: x_i \in \{head, tail\}\}$.
  • The realisation of five flips: $\vec x = \{head, tail, tail, tail, head\}$.

Do not mix up the realisation and the random variable. These are to different things.

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