Final answer:
The two requirements for a discrete probability distribution are that each probability must be between 0 and 1, and the sum of all probabilities must equal 1. Hence, the correct answer is D. Finite sample space and probabilities between 0 and 1.
Step-by-step explanation:
The question asks about the two requirements for a discrete probability distribution. A discrete probability distribution function must satisfy two main characteristics:
- Each probability is between zero and one, inclusive. This means the probability of any single event within the distribution must be greater than or equal to 0 and less than or equal to 1.
- The sum of the probabilities of all the distinct events must equal one. This ensures that one of the possible outcomes in the distribution will occur.
Therefore, the correct answer is D. Finite sample space and probabilities between 0 and 1. In the context of mutual exclusivity and independence:
- Mutually exclusive events cannot occur at the same time - that is, they do not share any common outcomes.
- On the other hand, independent events do not influence the occurrence of one another - the occurrence of one event does not affect the probability of the other.