Independent random variables

Two random variables are said to be independent if: $$ P(X=x|Y=y) = P(X=x) \qquad \forall \quad i,j $$ If two random variables are indpendent (

You should be able to explain in terms of conditional probability what it means for events to be independent.
You should be able to calculate the joint probability mass function, $f_{XY}(x,y)$ for a pair of independent variables, $X$ and $Y$, from the two individual marginal probability mass functions, $f_X(x)$ and $f_Y(y)$.