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Obtain the Probability Distribution of the Random Variable (1,1)(1,2)(1,3)(1,4)(1,5)(1,6) (1,1)(1,2)(1,3)(1,4)(1,5)(1,6)

Question 94

Multiple Choice

Obtain the probability distribution of the random variable.
-When two balanced dice are rolled, 36 equally likely outcomes are possible as shown below. (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Let X X denote the absolute value of the difference of the two numbers. Find the probability distribution of X. Give the probabilities as decimals rounded to three decimal places.


A)
xP(X=x) 00.16710.16720.16730.16740.16750.167\begin{array}{r|r}\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\\hline 0 & 0.167 \\1 & 0.167 \\2 & 0.167 \\3 & 0.167 \\4 & 0.167 \\5 & 0.167\end{array}

B)
xP(X=x) 10.27820.22230.16740.11150.056\begin{array}{r|r}\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\\hline 1 & 0.278 \\2 & 0.222 \\3 & 0.167 \\4 & 0.111 \\5 & 0.056\end{array}

C)
xP(X=x) 00.16710.25120.22230.16740.11150.05660.027\begin{array}{r|r}\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\\hline 0 & 0.167 \\1 & 0.251 \\2 & 0.222 \\3 & 0.167 \\4 & 0.111 \\5 & 0.056 \\6 & 0.027\end{array}

D)
xP(X=x) 00.16710.27820.22230.16740.11150.056\begin{array}{r|r}\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\\hline 0 & 0.167 \\1 & 0.278 \\2 & 0.222 \\3 & 0.167 \\4 & 0.111 \\5 & 0.056\end{array}

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