The Poisson distribution is a common discrete probability distribution that describes the number of random events that occur within a certain time period or region . It is named after the French mathematician Simone Denis Poisson.
The probability mass function of the Poisson distribution represents the probability of the number of occurrences of an event within a certain time period or region. If the random variable X obeys the Poisson distribution, it is recorded as The probability mass function of the Poisson distribution is:
P(X = k) = e^(-λ) * (λ^k) / k!
where e is the base of the natural logarithm and k is a non-negative integer.
The characteristics of Poisson distribution are:
1. Independence: The occurrence of events is independent of each other.
2. Rarity: In a relatively long time period or a large area, the probability of an event occurring is relatively small.
3. Stationarity: In the same time period or area, the average number of occurrences of events is constant.
4. Memorylessness: past events are independent of future events.
Poisson distribution has applications in many practical problems, such as:
1. The number of calls received by a telephone call center during a certain period of time.
2. The number of times a car passes through an intersection within a period of time.
3. The number of access requests the website receives in a day.
Through the Poisson distribution, the probabilities of these events can be modeled and analyzed, helping to make sound decisions and predictions.