Past exam of the year 1 of the computer science course of the University of Oxford / 2023 / Discrete mathematics, probability and continuous mathematics / 7 / a / i / Solution

The joint probability mass function is $p_{X,Y}(x,y)=\mathbb{P}(X=x,Y=y)$ for $(x,y)\in S^2$. It is nonnegative and its sum over $S^2$ equals one. Summing over one coordinate gives the other variable's marginal distribution.