Determine whether the distribution is a discrete probability distribution. \begin{tabular}{cc} \hline $\mathbf{x}$ & $\mathrm{P}(\mathbf{x})$ ㅁ⼝ \\ \hline 0 & 0.26 \\ \hline 1 & 0.12 \\ \hline 2 & 0.21 \\ \hline 3 & 0.25 \\ \hline 4 & 0.16 \\ \hline \end{tabular} Is the distribution a discrete probability distribution? A. Yes, because the sum of the probabilities is equal to 1. B. Yes, because each probability is between 0 and 1 , inclusive. C. No, because the-sum of the probabilities is not equal to 1. D. Yes, because the sum of the probabilities is equal to 1 and each probability is between 0 and 1 , inclusive (1) Time Remaining: 00:15.39 Next
Solution
Step 1 ：Given the distribution table, we need to determine whether it is a discrete probability distribution. The conditions for a distribution to be a discrete probability distribution are: each probability is between 0 and 1, inclusive, and the sum of all probabilities is equal to 1.
Step 2 ：First, we check if each probability is between 0 and 1, inclusive. Looking at the table, we can see that all probabilities are indeed between 0 and 1.
Step 3 ：Next, we need to check if the sum of all probabilities is equal to 1. We do this by adding all the probabilities: \(0.26 + 0.12 + 0.21 + 0.25 + 0.16\).
Step 4 ：The sum of the probabilities is 1. Therefore, both conditions for a discrete probability distribution are met.
Step 5 ：Final Answer: \(\boxed{\text{(D) Yes, because the sum of the probabilities is equal to 1 and each probability is between 0 and 1 , inclusive}}\)
