Question

Suppose that a pair of fair dice is thrown 1 time. Let the random variable X be the absolute difference of the dots that appear.

1) - What are the possible values of X?

2) - What is the sample space?

3) - Find the probability functions of X.

4) - Find the probability mass function

5) - Draw the graph for the probability mass function

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c:c:c} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & 0 & 1 & 2 & 3 & 4 & 5 \\ \hdashline 2 & 1 & 0 & 1 & 2 & 3 & 4 \\ \hdashline 3 & 2 & 1 & 0 & 1 & 2 & 3 \\ \hdashline 4 & 3 & 2 & 1 & 0 & 1 & 2 \\ \hdashline 5 & 4 & 3 & 2 & 1 & 0 & 1 \\ \hdashline 6 & 5 & 4 & 3 & 2 & 1 & 0 \\ \hdashline \end{array}$$

1) The possible values of $X$ are $0,1, 2, 3, 4,$ and $5.$

2)

$$S=\{0,1,2,3,4,5\}$$

3)

$$\def\arraystretch{1.5} \begin{array}{c:c} x & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline p(x) & 6/36 & 10/36 & 8/36 & 6/36 & 4/36 & 2/36 \\ \end{array}$$

4)

$$f(x) = \begin{cases} 6/36 &\ x=0 \\ 10/36&\ x=1 \\ 8/36&\ x=2 \\ 6/36&\ x=3 \\ 4/36&\ x=4 \\ 2/36&\ x=5 \\ \end{cases}$$

5)