Answered

IDNLearn.com helps you find the answers you need quickly and efficiently. Our community provides accurate and timely answers to help you understand and solve any issue.

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 :

GinnyAnsweridn
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.
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your search for answers ends at IDNLearn.com. Thanks for visiting, and we look forward to helping you again soon.