Roll a pair of four-sided dice, one red and one black, each of which has possible outcomes 1, 2, 3, 4 that have equal probabilities. Let X equal the outcome on the red die, and let Y equal the outcome on the black die.
(a) On graph paper, show the space of X and Y.
(b) Define the joint pmf on the space.
(c) Give the marginal pmf of X in the margin.
(d) Give the marginal pmf of Y in the margin.
(e) Are X and Y dependent or independent? Why or why not?