What of the following pairs of probability values would complete the following probability distribution? $\begin{array}{|l|c|c|c|c|c|c|}
\hline \mathrm{x} & -3 & -2 & -1 & 0 & 1 & 2 \
\hline \mathrm{P}(\mathrm{x}) & 0.09 & 0.18 & \mathrm{p}_{1} & \mathrm{p}_{2} & 0.14 & 0.23 \
\hline
\end{array}$

A) $\mathrm { p } _ { 1 } = 0.04 , \mathrm { p } _ { 2 } = 0.59$
B) $\mathrm { p } _ { 1 } = - 0.1 , \mathrm { p } _ { 2 } = 0.46$
C) $\mathrm { p } _ { 1 } = 0.36 , \mathrm { p } _ { 2 } = 0.36$
D) $\mathrm { p } _ { 1 } = 0 , \mathrm { p } _ { 2 } = 0.36$

Question

What of the following pairs of probability values would complete the following probability distribution? $\begin{array}{|l|c|c|c|c|c|c|}
\hline \mathrm{x} & -3 & -2 & -1 & 0 & 1 & 2 \
\hline \mathrm{P}(\mathrm{x}) & 0.09 & 0.18 & \mathrm{p}_{1} & \mathrm{p}_{2} & 0.14 & 0.23 \
\hline
\end{array}$

A) $\mathrm { p } _ { 1 } = 0.04 , \mathrm { p } _ { 2 } = 0.59$
B) $\mathrm { p } _ { 1 } = - 0.1 , \mathrm { p } _ { 2 } = 0.46$
C) $\mathrm { p } _ { 1 } = 0.36 , \mathrm { p } _ { 2 } = 0.36$
D) $\mathrm { p } _ { 1 } = 0 , \mathrm { p } _ { 2 } = 0.36$

Quizplus · Accepted Answer

Since the sum of all probabilities must be 1, we have:

$0.09 + 0.18 + p_1 + p_2 + 0.14 + 0.23 = 1$

Simplifying the left-hand side, we get:

$0.64 + p_1 + p_2 = 1$

$p_1 + p_2 = 0.36$

Since probabilities cannot be negative, the only choice that satisfies this condition is D, where $p_1 = 0$ and $p_2 = 0.36$.

What of the Following Pairs of Probability Values Would Complete