Question

Assume that the number of new visitors to a website in one hour is distributed as a Poisson random variable. The mean number of new visitors to the websile is 2.5 per hour. Complote parts (a) through

A) 0.146
B) 0.254
C) 0.334
D) 0.186

Answer 1

The question involves calculating probabilities based on the Poisson and exponential distributions, which are used to model random events occurring independently over time, such as visits to a website or calls to a police station.

Step-by-step explanation:

The question involves the application of the Poisson and exponential distributions for modeling the number of visits or calls and the time between events, respectively. In these scenarios, we calculate probabilities using the known mean rates of occurrence. Given a mean rate, we can derive various probabilities related to the distribution, such as the probability of a certain number of events occurring within a specific period, or the probability that the time between events exceeds or is less than a given duration. These calculations are commonplace in fields like healthcare, email management, and emergency services.

For example, if we know that an emergency room gets an average of five patients per hour, we can calculate the probability that more than five patients will arrive in an hour using the Poisson distribution, because we expect the number of arrivals to be random and distributed independently over time.