Past exam of the year 1 of the computer science course of the University of Oxford / 2013 / Discrete mathematics, probability and continuous mathematics / 8 / c / i

This numbered item specifies the model used below. A convenient sample space is the collection of $36$ ordered pairs $(s_1,s_2)\in \{1,\dots ,6{\}}^2$, each with probability $1/36$. The corresponding random variables are determined by the sum and difference. Inverting the two equations givesThus a candidate pair $(X,Y)=(i,j)$ is possible exactly when $(i+j)/2$ and $(i-j)/2$ are both integers between $1$ and $6$. In particular, $i$ and $j$ must have the same parity. This inverse description will determine the joint probability mass function.