What is the difference between saying X is a random variable following normal distribution and X is normally distributed. Is the random variable implicit or is X in the second case some other entity?
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2 Answers
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Only a random variable can follow a distribution. If “X is normally distributed” it needs to be a random variable. Those terms mean the same thing.
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Without more context "X is normally distributed" could either mean X is a variable taken randomly from a normal distribution or it could be referenced as an array or matrix in which the values in it are normally distributed.
It really depends on the context as far as I can tell.
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1$\begingroup$ Random variable cannot be “taken” from a distribution. Same with values of an array or a matrix, they cannot “be“ normally distributed, the matrix can be thought as a random matrix, a matrix of random variables, but the values you observe are just numbers, not random variables. The values can be thought as of realizations of random variables. $\endgroup$– TimCommented Sep 5, 2021 at 17:07