A four-sided die is tossed twice. The difference of the outcomes is denoted by X
and the maximum value by Y .
(a) Find the joint PMF. Tabulate it (write it on a table.)
(b) Find the marginal PMFs.
The possible differences are 0,1,2,3,4,5, and the maximum 1,2,3,4,5,6. Let the (d,m) denote the event that the difference is d and the maximum is m. For task a) you need to evaluate the probability of (d,m) for d=0 .. 5 and m=1 .. 6 and tabulate the probabilities.
I will do the first of these for you. Let the outcome of the first toss be x and that of the second be y. The event (0,1) can only occur if both x and y=1, which occurs with probability (1/6)(1/6)=1/36.
CB