Answer(s): The interval is the same for probability failure as in success in exceeding the size of the interval.
Explanation:
The option that does not satisfy the properties of a Poisson process is:
- The interval is the same for probability failure as in success in exceeding the size of the interval.
In a Poisson process, the interval is considered to be fixed, meaning that it remains the same regardless of the outcome of success or failure. The probability of success in an interval is the same for all intervals of equal size and proportional to the length of the interval.
However, in the given option, the interval for probability failure is different from the interval for success in exceeding the size of the interval. This violates the property of a Poisson process where the interval remains the same for both success and failure probabilities.
The other three options listed are consistent with the properties of a Poisson process:
- Success is presented as an integer between zero and infinity, which aligns with the discrete nature of a Poisson process.
- The number of successes counted in nonoverlapping intervals are independent, meaning that the occurrence of a success in one interval does not affect the occurrence of success in another interval.
- The probability of success in an interval is the same for all intervals of equal size and proportional to the length of the interval. This reflects the characteristic of a Poisson process where the probability of success remains constant across equal-sized intervals.
By elimination, we can conclude that the option "the interval is the same for probability failure as in success in exceeding the size of the interval" does not satisfy the properties of a Poisson process.