Questions: Determine whether the distribution is a discrete probability distribution. If not, state why. (a) B x P(x) 0 0.36 1 0.27 2 0.16 3 0.07 4 0.14 (b) 몬 x P(x) 0 0.42 1 0.19 2 0.12 3 0.04 4 0.15 (a) Is the distribution a discrete probability distribution? A. Yes, because the sum of the probabilities is equal to 1 and each probability is between 0 and 1, inclusive. B. No, because the sum of the probabilities is not equal to 1 and each probability is not between 0 and 1, inclusive. C. No, because each probability is not between 0 and 1, inclusive. D. Yes, because the sum of the probabilities is equal to 1. E. No, because the sum of the probabilities is not equal to 1. F. Yes, because each probability is between 0 and 1, inclusive.

Solution Steps

For Distribution A, we have the following probabilities:

\[ \begin{align_} P(0) & = 0.36 \\ P(1) & = 0.27 \\ P(2) & = 0.16 \\ P(3) & = 0.07 \\ P(4) & = 0.14 \\ \end{align_} \]

First, we check if each probability \( P(x) \) is between 0 and 1:

\[ 0 \leq P(x) \leq 1 \quad \text{for all } x \]

Next, we calculate the sum of the probabilities:

\[ \sum P(x) = 0.36 + 0.27 + 0.16 + 0.07 + 0.14 = 1.00 \]

Since the sum of the probabilities equals 1 and each probability is within the range \([0, 1]\), we conclude that Distribution A is a discrete probability distribution.

For Distribution B, we have the following probabilities:

\[ \begin{align_} P(0) & = 0.42 \\ P(1) & = 0.19 \\ P(2) & = 0.12 \\ P(3) & = 0.04 \\ P(4) & = 0.15 \\ \end{align_} \]

Again, we check if each probability \( P(x) \) is between 0 and 1:

\[ 0 \leq P(x) \leq 1 \quad \text{for all } x \]

Next, we calculate the sum of the probabilities:

\[ \sum P(x) = 0.42 + 0.19 + 0.12 + 0.04 + 0.15 = 0.92 \]

Since the sum of the probabilities does not equal 1, Distribution B is not a discrete probability distribution.

Final Answer