What is a cumulative Poisson probability?
A cumulative Poisson probability refers to the probability that the Poisson random variable (X) falls within a certain range. For example, consider the probability of getting AT MOST n successes in a Poisson experiment. Here, n would be a Poisson random variable. And the cumulative Poisson probability would be the probability that n falls within the range of 0 and n. For instance, we might be interested in the number of phone calls received in an hour by a receptionist. Suppose we knew that she received 1 phone call per hour on average. We might ask: What is the likelihood that she will receive AT MOST 1 phone call next hour? The probability of getting AT MOST 1 phone call in the next hour would be an example of a cumulative Poisson probability. Note: The cumulative Poisson probability in this example is equal to the probability of getting zero phone calls PLUS the probability of getting one phone call. Thus, the cumulative Poisson probability would equal 0.368 + 0.368 or 0.736 (see th
