Determine whether the distribution is a discrete probability distribution.

| x | P(x) |
|---|-------|
| 0 | 0.36 |
| 1 | 0.24 |
| 2 | 0.18 |
| 3 | 0.13 |
| 4 | 0.09 |

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

The distribution is a discrete probability distribution because each probability is between 0 and 1 and the sum of all probabilities equals 1. Thus, the correct answer is B. Both key conditions for a discrete probability distribution are satisfied in this case.
;

Answered by Anonymous | 2025-07-04

Each probability must be between 0 and 1.
The sum of all probabilities must equal 1.
The sum of the given probabilities is 0.36 + 0.24 + 0.18 + 0.13 + 0.09 = 1.0 .
Therefore, the distribution is a discrete probability distribution because both conditions are met. The answer is B.

Explanation

Analyze the problem and data We are given a table that shows the probability P ( x ) for different values of x . To determine if this is a discrete probability distribution, we need to check two conditions:

Each probability P ( x ) must be between 0 and 1, inclusive (i.e., 0 ≤ P ( x ) ≤ 1 ).

The sum of all probabilities must equal 1.

Verify that each probability is between 0 and 1 First, let's check if each probability is between 0 and 1:



P ( 0 ) = 0.36 , which is between 0 and 1.
P ( 1 ) = 0.24 , which is between 0 and 1.
P ( 2 ) = 0.18 , which is between 0 and 1.
P ( 3 ) = 0.13 , which is between 0 and 1.
P ( 4 ) = 0.09 , which is between 0 and 1.

So, the first condition is satisfied.

Calculate the sum of the probabilities Next, let's calculate the sum of the probabilities:

S = 0.36 + 0.24 + 0.18 + 0.13 + 0.09
From the calculation tool, we know that the sum is:
S = 1.0
So, the second condition is also satisfied.

Conclusion Since both conditions are satisfied (each probability is between 0 and 1, and the sum of the probabilities is equal to 1), the given distribution is a discrete probability distribution. Therefore, the correct answer is B.

Examples
Discrete probability distributions are used in various real-life scenarios. For example, in quality control, we can use a discrete probability distribution to model the number of defective items in a batch. In finance, it can be used to model the number of successful trades in a given period. In sports, it can be used to model the number of goals scored by a team in a match. Understanding these distributions helps in making informed decisions based on probabilities.

Answered by GinnyAnswer | 2025-07-04