Final answer:
The given distribution is not a discrete probability distribution because the probabilities are not between 0 and 1 and their sum does not equal 1.
Step-by-step explanation:
To determine whether the given distribution is a discrete probability distribution, we need to check two main conditions: First, the probability P(x) for each outcome x must be between 0 and 1 inclusive, and second, the sum of all probabilities must equal 1. In the case provided, the probabilities for the values of x (-3, 1, 5) are given as 12, 14, 18, which instantly seems incorrect because these numbers are not probabilities, as they are greater than 1 and not between 0 and 1. Additionally, when we add these numbers (12 + 14 + 18), we get a sum of 44, which is not equal to 1. Therefore, the given distribution is not a discrete probability distribution, as it fails both essential characteristics: proper probability values and the sum of probabilities equaling 1.