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>.

Solution

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

 Solution (source code)