Random variable or number?

Question

We have the common probability distribution of two random variables $X$ and $Y$ :

At the terms: $$Y, \ y_j, \ E(Y), \ E(Y\mid X), \ E(Y\mid X=x_i), \ E_X(E(Y\mid X))$$ is just $Y$ a random variable and all the others are numbers?

Answer 1

$Y$ is defined as a random variable. You have not defined $y_j$, but if it is the $Y$ value from the $j^{th}$ draw of $X,Y$ it is a number. All the expectations are numbers that are computed from your probability table except $E(Y|X=x_i)$ which is a function of $x_i$.