# probability – Strange Statement/Exercise about random variables

So the statement i don’t understand is:

Let $$X$$ be a discrete random variable, then there exists another (discrete) random variable $$X’$$ on a probability space with the same distribution.

The only thing that occurs to me is that if i define $$X’:=X$$ , then obviously they have the same distribution. But this just looks too simple.

I hope someone could help me understand/proof the statement