A four-sided (tetrahedral) die has a different number 1, 2, 3 or 4 affixed to each face. On any given roll, each of the four numbers is equally likely to occur (face down). An experiment consists of rolling the die twice and recording the two values obtained in order. Random variable X represents the lesser of the two values, random variable Y represents the first value minus the second.

(a) Construct the sample space for the experiment.

(b) Construct the induced sample space for (X, Y ).

(c) Construct the probability distributions for X and Y .

(d) Obtain X, Y , X, Y and Cov(X, Y ) = XY .