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Statistics and Probability

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Moderate

Matching Probability Mass Function to a Random Variable

STATS-JF9NJR

Let $X$ be the sum of the rolls of two six-sided dice. Which of the following would accurately describe a probability mass function $p(x)$ of $X$?

i.

$$ p(x)=\begin{cases} \frac{1}{36} &\mbox{if } x=2 \mbox{ or } 12\\\ \frac{2}{36} &\mbox{if } x=3 \mbox{ or } 11\\\ \frac{3}{36} &\mbox{if } x=4 \mbox{ or } 10\\\ \frac{4}{36} &\mbox{if } x=5 \mbox{ or } 9\\\ \frac{5}{36} &\mbox{if } x=6 \mbox{ or } 8\\\ \frac{6}{36} &\mbox{if } x=7 \end{cases} $$

ii.

$$ p(x)=\begin{cases} \frac{x-1}{36} &\mbox{if } 2\leq x\leq 7\\\ \frac{13-x}{36} &\mbox{if } 8\leq x\leq12 \end{cases} $$

iii.

$$ p(x)=\begin{cases} \frac{2x-2}{72} &\mbox{if $x$ is an integer between (and including) 2 and 7}\\\ \frac{13-x}{36} &\mbox{if $x$ is an integer between (and including) 8 and 12} \end{cases} $$

iv. $p(x)$ is such that its corresponding Bar Graph looks like

v. $p(x)$ is such that its graph looks like

A

i, ii, iii, iv, v

B

i, ii, iv, v

C

i, ii, iii, iv

D

i, iii, iv

E

ii, iv

F

iii, iv