To determine if a set of values forms a discrete probability distribution, there are specific properties that must be satisfied. Here are the step-by-step requirements:
1. Nonnegativity: Each probability value must be between 0 and 1, inclusive. This ensures that no event has a negative probability and no probability exceeds certainty.
- Mathematically, this is represented as [tex]\(0 \leq P(x) \leq 1\)[/tex].
2. Normalization: The sum of all the probabilities of the possible outcomes must equal 1. This guarantees that the total probability is distributed among all possible outcomes in a way that encompasses the entire sample space.
- Mathematically, this is expressed as [tex]\(\sum P(x) = 1\)[/tex].
Considering the above properties, the correct requirements for a discrete probability distribution are:
- [tex]\(0 \leq P(x) \leq 1\)[/tex]
- [tex]\(\sum P(x) = 1\)[/tex]
Thus, the correct answers are:
A. [tex]\( 0 \leq P(x) \leq 1 \)[/tex]
B. [tex]\(\sum P(x) = 1 \)[/tex]
