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We do not really know the true distribution of random variable. We only know the samples from true distribution and hence know the sample distribution.

In that case, what is the support of random variable? If it is all possible values that a random variable can take, how will we know that if we only know sample distribution and not true distribution (sample distribution only has some samples, not all possible values of a random variable)?

Curious
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  • I think you are misinterpreting what a random variable is, but I can't find out how to correct you. Also - if I say that $X$ is exponential with parameter $\lambda$ then we do indeed know its distribution. Compare this to sampling a process. – Sean Roberson Dec 02 '22 at 03:06
  • You can know the support without needing a sample. Take the exponential with parameter $\lambda$. It's support is the non-negative real line. – mark leeds Dec 02 '22 at 05:33
  • Btw. The support is formally defined here. That question was not uninteresting an still has no formal answer. – Kurt G. Dec 02 '22 at 06:32

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