Answer to Question #340139 in Statistics and Probability for Maneo

Question #340139

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




1
Expert's answer
2022-05-24T17:54:21-0400
123456101234521012343210123432101254321016543210\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 XX are 0,1,2,3,4,0,1, 2, 3, 4, and 5.5.


2)

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

3)


x012345p(x)6/3610/368/366/364/362/36\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)={6/36 x=010/36 x=18/36 x=26/36 x=34/36 x=42/36 x=5f(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)




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