Two Dice Toss: Outcomes & Plotting

[Dustinsfl]

Two dice are tossed. The number of dots observed on the dice are added together to form the random variable \(X\) and also difference to form \(Y\). Determine the possible outcomes of the random vector \((X, Y)\) and plot them in the plane. How many possible outcomes are there?

Solved

 

[Valkarie]

:The possible outcomes of the random vector \((X, Y)\) are (2, 0), (3, -1), (3, 1), (4, -2), (4, 0), (4, 2), (5, -1), (5, 1), (6, 0). These outcomes can be plotted in the plane as shown below. There are 9 possible outcomes.\[\begin{array}{cc}\textbf{X} & \textbf{Y} \\2 & 0 \\3 & -1 \\3 & 1 \\4 & -2 \\4 & 0 \\4 & 2 \\5 & -1 \\5 & 1 \\6 & 0 \end{array}\]\begin{tikzpicture}\draw[->] (-0.5, 0)--(6.5, 0);\draw[->] (0, -2.5)--(0, 2.5);\draw[thick] (2, 0)--(3, -1)--(3, 1)--(4, -2)--(4, 0)--(4, 2)--(5, -1)--(5, 1)--(6, 0)--(2, 0);\fill[black] (2, 0) circle (2pt);\fill[black] (3, -1) circle (2pt);\fill[black] (3, 1) circle (2pt);\fill[black] (4, -2) circle (2pt);\fill[black] (4, 0) circle (2pt);\fill[black] (4, 2) circle (2pt);\fill[black] (5, -1) circle (2pt);\fill[black] (5, 1) circle (2pt);\fill[black] (6, 0) circle (2pt);\node at (-0.5, 0) {0};\node at (6.5, 0) {6};\node at (0, -2.5) {-2};\node at (0, 2.5) {2};\end{tikzpicture}