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

question 121

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

Let $X$ denote the smaller of the two numbers. If both dice come up the same number, then $X$ equals that common value. Find the probability distribution of $X$ . Leave your probabilities in fraction form.

• A)
• \(\begin{array}{r|r}
• x & P(X=x) \\
• \hline 1 & 5 / 18 \\
• 2 & 1 / 4 \\
• 3 & 7 / 36 \\
• 4 & 5 / 36 \\
• 5 & 1 / 9 \\
• 6 & 1 / 36
• \end{array}\)
• B)
• \(\begin{array}{r|r}
• \mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\
• \hline 1 & 11 / 36 \\
• 2 & 1 / 4 \\
• 3 & 7 / 36 \\
• 4 & 5 / 36 \\
• 5 & 1 / 12 \\
• 6 & 1 / 36
• \end{array}\)
• C)
• \(\begin{array}{r|r}
• x & P(X=x) \\
• \hline 1 & 5 / 18 \\
• 2 & 2 / 9 \\
• 3 & 1 / 6 \\
• 4 & 1 / 9 \\
• 5 & 1 / 18 \\
• 6 & 0
• \end{array}\)
• D)
• \(\begin{array}{r|r}
• x & P(X=x) \\
• \hline 1 & 1 / 6 \\
• 2 & 1 / 6 \\
• 3 & 1 / 6 \\
• 4 & 1 / 6 \\
• 5 & 1 / 6 \\
• 6 & 1 / 6
• \end{array}\)

Understand the impact of environmental worldviews on societal attitudes toward nature and resource management.

Understand the foundational theories and researchers in organizational behavior.

Recognize the importance of managing employee behavior in public organizations for effective governance.

Comprehend the significance of organizational behavior in formulating strategies for human resource management.

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