copy of a random variable X

Question

If we have a random variable X,

What does mean by X′ denotes an independent copy of X.

by simple example.

thanks

Answer 1

It means that the distribution of $X$ is the same as the distribution of $X'$ and that $X$ and $X'$ are independent.

So, if $X$ is a continuous random variable with pdf $p_X$, then $X'$ is a continuous random variable with pdf $p_{X'} = p_X$, and for each pair of events $S_1$ and $S_2$, you have $$P(X \in S_1\land X' \in S_2) = P(X\in S_1)\cdot P(X'\in S_2)= P(X\in S_1)\cdot P(X\in S_2)$$