Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Discover precise answers to your questions from a wide range of 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 Probability Distribution C \\
\hline [tex]$X$[/tex] & [tex]$P(x)$[/tex] \\
\hline 1 & 0.16 \\
\hline 2 & 0.39 \\
\hline 3 & 0.18 \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
To determine which of the given probability distributions are valid, we need to verify if the sum of probabilities in each distribution equals 1. A valid probability distribution must have probabilities that sum to exactly 1.

Let's analyze each distribution in detail:

### Probability Distribution A:

Given probabilities:
[tex]\[P(X = 1) = 0.42\][/tex]
[tex]\[P(X = 2) = 0.38\][/tex]
[tex]\[P(X = 3) = 0.13\][/tex]
[tex]\[P(X = 4) = 0.07\][/tex]

Sum of probabilities:
[tex]\[0.42 + 0.38 + 0.13 + 0.07 = 1.0\][/tex]

Since the sum is 1.0, Distribution A is a valid probability distribution.

### Probability Distribution B:

Given probabilities:
[tex]\[P(X = 1) = 0.27\][/tex]
[tex]\[P(X = 2) = 0.28\][/tex]
[tex]\[P(X = 3) = 0.26\][/tex]
[tex]\[P(X = 4) = 0.27\][/tex]

Sum of probabilities:
[tex]\[0.27 + 0.28 + 0.26 + 0.27 = 1.08\][/tex]

Since the sum is 1.08, which is not equal to 1, Distribution B is not a valid probability distribution.

### Probability Distribution C:

Given probabilities:
[tex]\[P(X = 1) = 0.16\][/tex]
[tex]\[P(X = 2) = 0.39\][/tex]
[tex]\[P(X = 3) = 0.18\][/tex]

Sum of probabilities:
[tex]\[0.16 + 0.39 + 0.18 = 0.73\][/tex]

Since the sum is 0.73, which is not equal to 1, Distribution C is not a valid probability distribution.

### Summary:

- Probability Distribution A: Valid (sum = 1.0)
- Probability Distribution B: Not Valid (sum = 1.08)
- Probability Distribution C: Not Valid (sum = 0.73)

Thus, the only valid probability distribution among the given options is Probability Distribution A.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.