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)
• \(\begin{array}{r|r}
• x & P(X=x) \\
• \hline 1 & 1 / 6 \\
• 2 & 1 / 6 \\
• 3 & 1 / 6 \\
• 4 & 1 / 6 \\
• 5 & 1 / 6 \\
• 6 & 1 / 6
• \end{array}\)

---

Definitions:

Refractory Period

In neural processing, a brief resting pause that occurs after a neuron has fired; subsequent action potentials cannot occur until the axon returns to its resting state. In human sexuality, a resting period that occurs after orgasm, during which a person cannot achieve another orgasm.

Asexual

Describes an individual who does not experience sexual attraction to others.

American System

A historical economic plan in the United States that advocated for a strong role for federal government in the economy, emphasizing protective tariffs, national bank, and infrastructure improvements.

Federal Funds

Refers to reserves that banks lend to each other overnight to maintain their reserve requirements, often influencing interest rates.