Final answer:
The distribution presented is a discrete probability distribution because each probability is between 0 and 1, and the sum of all probabilities equals exactly 1.
Step-by-step explanation:
To determine whether a given distribution is a discrete probability distribution, we must check two essential characteristics:
Each probability P(X = x) must be between 0 and 1, inclusive.
The sum of all the probabilities must equal 1.
Looking at the provided probabilities for the values of X (-1, 1, 8), the probabilities are 0.34, 0.29, and 0.37, respectively. Checking the first condition, we can see that each probability is indeed between 0 and 1. To check the second condition, we add up the probabilities:
0.34 + 0.29 + 0.37 = 1.00
Since the sum is 1, both conditions for a discrete probability distribution are satisfied. Therefore, this distribution is indeed a discrete probability distribution.