Dice rolls: Explicit calculation of max/min

Let \(X_1\) and \(X_2\) be the number obtained on two rolls of a fair die. Let \(Y_1=\max(X_1,X_2)\) and \(Y_2=\min(X_1,X_2)\).

1. Display the joint distribution tables for \( (X_1,X_2)\).
2. Display the joint distribution tables for \( (Y_1,Y_2)\).
3. Find the distribution of \(X_1X_2\).

Combination of [Pitman, p. 159 #4 and #5]