Question

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 1

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

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.