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)

(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)

(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)

(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)

(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)

(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)

Let

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)

\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}

\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}

\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}

\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}

Use Random-Variable Notation to Represent the Event {3<Y<5}\{ 3 < Y < 5 \}{3<Y<5}

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Use Random-Variable Notation to Represent the Event $\{ 3 < Y < 5 \}$

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