Suppose that we roll a pair of balanced dice and X is the number of dice that come up 1, and Y is the number of dice that come up 4, 5, or 6.
(a) Draw a diagram like that of Figure 1 showing the values of X and Y associated with each of the 36 equally likely points of the sample space.
(b) Construct a table showing the values of the joint probability distribution of X and Y.