Short Answer 
A probability distribution describes the likelihood of outcomes and must meet the criteria of summing to 1 and having non-negative values. In the analysis, only Distribution A is valid, as it is the only one that sums to 1 without any negative probabilities.
Step 1: Understanding Probability Distributions
A probability distribution is a function that describes the likelihood of different outcomes in a random experiment. For a distribution to be valid, it must meet certain criteria, primarily that all probabilities sum up to 1. Additionally, all probabilities must be non-negative, meaning they cannot be less than zero.
Step 2: Analyzing the Provided Distributions
Each distribution must be evaluated based on the criteria mentioned. In the provided options, we can analyze each one based on their probability values:
- Distribution A: Probabilities add to 1 (0.45 + 0.16 + 0.39 = 1, valid).
- Distribution B: Includes a negative probability (-0.14, invalid).
- Distribution C: Contains a negative probability (-0.87, invalid).
- Distribution D: Sums to 2.81 (invalid as it exceeds 1).
Step 3: Conclusion on Validity
From the analysis, only Distribution A satisfies the requirement of being a valid probability distribution. It is the only option where the probabilities add up to 1 without any negative values. Therefore, for anyone studying probability distributions, remember to check for the total sum and the sign of each probability to determine validity.