Determine whether the distribution is a discrete probability distribution.

X P (x)

0 0.13

1 0.27

2 0.18

3 0.27

4 0.13

Is the probabily distribution a discrete distibution? why?

A - Yes, because the distribution is symmetric.

B - Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive.

C - No, beacause some of the probabilities have values greater than 1 or less than 0.

D - No, because the total probability is not equal to 1

Answer: D - No, because the total probability is not equal to 1.

Step-by-step explanation:

If X is a random variable with a discrete probability distribution, then

1. 0≤P (x) ≤1, for any value of x.

2. The sum of the probabilities must be equal to 1.

The given discrete probability distribution:

X P (x)

0 0.13

1 0.27

2 0.18

3 0.27

4 0.13

Here, each probability is greater than 0 and less than 1, so first condition is satisfied.

The sum of probabilities = 00.13+0.27+0.18+0.27+0.13=0.98≠ 1

It means, the second condition is not satisfied.

Thus, the probability distribution is a discrete distribution.

Hence, the correct answer is : D - No, because the total probability is not equal to 1.