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I sometimes think that random variables are variables whose value are random. For example, normally, x =1 or x =0

However, if x is a random variable, then x can be 1 with say, half probability, and 0 with half probability.

So it's basically like the definition of limit. Intuitively, we say limit of f(x) when x approach x0 as what it actually says. We just put complex logical definition on top of that. Things like for every epsilon there is delta, bla bla bla....

So I wonder if my intuitive definition of random variable has merit and how to reconcile that with the more robust definition of random variable?

user4951
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  • I'm not sure what you are trying to achive here. Intuitivly, A random variable is a variable whose value depends on unknown events. Random variable has a pretty precise and rigour definition (you can find it easily). – Eminem Aug 03 '20 at 06:44
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    Nope. Little merit. You're introducing the notion of limit where none is needed, and in many cases none is appropriate. The outcome of a single coin flip is a random variable even if it is only flipped once. Nothing about "...in the limit...." – David G. Stork Aug 03 '20 at 06:47
  • I think the limit thing was just an example, where he showed that the limit, even though defined rigourously, has an intuitive interpretation. It was not meant to be the intuition behind a random variable. – Mushu Nrek Aug 03 '20 at 07:08
  • I don't understand what you say about limits, but I think your intuitive understanding of random variable is correct. As for reconciling it with the rigorous definition, that's harder. People worked with unsatisfactory notions of random variable for many years before Kolmogorov came up with the definition in the 1930's. If you know some measure theory, it's pretty clear that this is the right definition, but personally, I always think of a random variable as encoding the result of some experiment. – saulspatz Aug 03 '20 at 07:11

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