Final answer:
The given distribution is not a discrete probability distribution, as the sum of the probabilities (3/8 + 1/3 + 3/4) exceeds one, violating the requirement that the total probability must be exactly one.
Step-by-step explanation:
To determine whether or not the distribution is a discrete probability distribution, we must check two essential characteristics. The first characteristic is that each probability value, P(X = x), must be between zero and one (inclusive). The second characteristic is that the sum of all the probability values must equal one.
For the given distribution with x = 2, 4, 8 and P(X = x) being 3/8, 1/3, and 3/4 respectively, we immediately notice an issue. When we calculate the sum of the probabilities, we have:
3/8 + 1/3 + 3/4 = 0.375 + 0.333 + 0.75 = 1.458
The sum of these probabilities is greater than one which violates the second characteristic of a discrete probability distribution. Therefore, the given distribution is not a discrete probability distribution.