Questions: Determine whether the distribution is a discrete probability distribution. x 100 200 300 400 500 P(x) 0.1 0.1 0.1 0.1 0.1 Is the distribution a discrete probability distribution? A. No, because the sum of the probabilities is not equal to 1. B. No, because each probability is not between 0 and 1, inclusive. C. Yes, because the sum of the probabilities is equal to 1. D. Yes, because the sum of the probabilities is equal to 1 and each probability is between 0 and 1, inclusive.

Determine whether the distribution is a discrete probability distribution.
x 100 200 300 400 500
P(x) 0.1 0.1 0.1 0.1 0.1

Is the distribution a discrete probability distribution?
A. No, because the sum of the probabilities is not equal to 1.
B. No, because each probability is not between 0 and 1, inclusive.
C. Yes, because the sum of the probabilities is equal to 1.
D. Yes, because the sum of the probabilities is equal to 1 and each probability is between 0 and 1, inclusive.

Transcript text: te Probability Distributions ework.aspx?homeworkld=682415246\&questionld=1\&flushed=false\&cld=7994920\¢erwin=yes jachelle henry 11/08/24 11:23 PI Question 5, 6.3.15 HW Score: $30 \%, 3.6$ of 12 points Points: 0 of 1 Determine whether the distribution is a discrete probability distribution. \begin{tabular}{crrrrr} x & 100 & 200 & 300 & 400 & 500 \\ $\mathbf{P}(\mathrm{x})$ & 0.1 & 0.1 & 0.1 & 0.1 & 0.1 \end{tabular} Is the distribution a discrete probability distribution? A. No, because the sum of the probabilities is not equal to 1 . B. No, because each probability is not between 0 and 1 , inclusive. C. Yes, because the sum of the probabilities is equal to 1. D. Yes, because the sum of the probabilities is equal to 1 and each probability is between 0 and 1 , inclusive. example Get more help - Clear all Check answe

Solution

Solution Steps

To determine if the given distribution is a discrete probability distribution, we need to check two conditions: (1) the sum of all probabilities should be equal to 1, and (2) each probability should be between 0 and 1, inclusive. If both conditions are satisfied, then it is a discrete probability distribution.

Step 1: Check the Sum of Probabilities

We have the probabilities $ P(x) = [0.1, 0.1, 0.1, 0.1, 0.1] $. The sum of these probabilities is calculated as follows:

\[ \sum P(x) = 0.1 + 0.1 + 0.1 + 0.1 + 0.1 = 0.5 \]

Since $ 0.5 \neq 1 $, the first condition for a discrete probability distribution is not satisfied.

Step 2: Check the Validity of Each Probability

Next, we check if each probability is within the range $ [0, 1] $. Each probability is $ 0.1 $, which satisfies the condition $ 0 \leq P(x) \leq 1 $. Therefore, the second condition is satisfied.

Step 3: Conclusion

Since the sum of the probabilities is not equal to 1, we conclude that the distribution does not meet the criteria for a discrete probability distribution.