Why is $mathbb E(X)=sum_{i=1}^{n}x_i P(x_i)$?

If $X$ is a random variable and $x$’s are the realizations form $X$ and

• $N$ is the population size

• $n$ is the sample size

Which one is correct

• $mathbb E(X)=sum_{i=1}^{N}x_i P(x_i)$

or

• $mathbb E(X)=sum_{i=1}^{n}x_i P(x_i)$ .

I know the latter is the correct one . But don’t know why ?