Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Which of the following is a valid probability distribution?

\begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{ Probability Distribution A } \\
\hline [tex]$X$[/tex] & [tex]$P(x)$[/tex] \\
\hline 1 & 0.42 \\
\hline 2 & 0.38 \\
\hline 3 & 0.13 \\
\hline 4 & 0.07 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{ Probability Distribution B } \\
\hline [tex]$X$[/tex] & [tex]$P(x)$[/tex] \\
\hline 1 & 0.27 \\
\hline 2 & 0.28 \\
\hline 3 & 0.26 \\
\hline 4 & 0.27 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{ Probability Distribution C } \\
\hline [tex]$X$[/tex] & [tex]$P(x)$[/tex] \\
\hline 1 & 0.16 \\
\hline 2 & 0.39 \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
To determine which of the provided probability distributions is valid, we need to verify that the sum of the probabilities for each distribution equals 1. This property is essential for any valid probability distribution.

Let's check each distribution step-by-step.

### Probability Distribution A:
[tex]\[ \begin{array}{|c|c|} \hline X & P(X) \\ \hline 1 & 0.42 \\ \hline 2 & 0.38 \\ \hline 3 & 0.13 \\ \hline 4 & 0.07 \\ \hline \end{array} \][/tex]
Sum of probabilities for Distribution A:
[tex]\[ 0.42 + 0.38 + 0.13 + 0.07 = 1.0 \][/tex]
The sum is 1.0, so Distribution A is a valid probability distribution.

### Probability Distribution B:
[tex]\[ \begin{array}{|c|c|} \hline X & P(X) \\ \hline 1 & 0.27 \\ \hline 2 & 0.28 \\ \hline 3 & 0.26 \\ \hline 4 & 0.27 \\ \hline \end{array} \][/tex]
Sum of probabilities for Distribution B:
[tex]\[ 0.27 + 0.28 + 0.26 + 0.27 = 1.08 \][/tex]
The sum is 1.08, which is not equal to 1. Therefore, Distribution B is not a valid probability distribution.

### Probability Distribution C:
[tex]\[ \begin{array}{|c|c|} \hline X & P(X) \\ \hline 1 & 0.16 \\ \hline 2 & 0.39 \\ \hline \end{array} \][/tex]
Sum of probabilities for Distribution C:
[tex]\[ 0.16 + 0.39 = 0.55 \][/tex]
The sum is 0.55, which is not equal to 1. Therefore, Distribution C is not a valid probability distribution.

### Conclusion:
Among the given probability distributions, only Probability Distribution A is a valid distribution because its probabilities sum to 1.
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.