The correct answer is D. All of the mentioned.
The Poisson distribution is a probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known average rate and independently of the time since the last event. It is named after Siméon Denis Poisson, who first published it in 1837.
The Poisson distribution is often used to model the number of events that occur in a given time interval, such as the number of phone calls received by a call center in an hour, the number of errors in a software program, or the number of radioactive decays in a given sample. It can also be used to model the number of events that occur in a given area, such as the number of car accidents on a highway in a day, the number of people who visit a website in a week, or the number of bacteria in a colony.
The Poisson distribution is a good model for events that occur with a low probability and are independent of each other. For example, the number of phone calls received by a call center in an hour is a good example of an event that occurs with a low probability. The probability of receiving a phone call in a given minute is very low, but the number of phone calls received in an hour is likely to be a Poisson random variable.
The Poisson distribution is also a good model for events that occur with a known average rate. For example, the number of errors in a software program is a good example of an event that occurs with a known average rate. The average number of errors in a software program is likely to be a Poisson random variable.
The Poisson distribution is a versatile tool that can be used to model a variety of events. It is a good model for events that occur with a low probability and are independent of each other. It is also a good model for events that occur with a known average rate.