The Poisson distribution is a probability distribution used to model the occurrence of events in a fixed interval, characterized by a parameter λ representing the average number of events. It is particularly useful for independent events in fields like telecommunications and disaster prediction, although it has limitations, including the assumption of independent and constant event rates. Understanding its characteristics and limitations is essential for effective application in various domains.

1. Poission Distribution
Presented By:
K.Sai Aashritha
23P61A6798
CSD-B

2. Introduction to Poisson Distribution
• 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.
• It is particularly useful for modeling rare events or events that
occur independently of one another.
• The distribution is characterized by a single parameter, λ
(lambda), which represents the average number of events in the
given interval.

3. Characteristics of Poisson Distribution
• The mean and variance of a Poisson distribution are both equal
to λ.
• The probability of observing k events in an interval is given by
the formula: P(X=k) = (λ^x)
• e^(-λ)) / x!.

4. When to Use Poisson Distribution
• The Poisson distribution is best used when events occur
independently and the average rate of occurrence is known.
• It is commonly applied in fields such as telecommunications,
traffic flow, and natural disaster prediction.
• Situations involving counts of occurrences over time, such as the
number of emails received per hour, are ideal for this model.

6. Limitations of Poission Distribution:
While the Poisson Distribution is powerful, it has limitations. It
assumes events occur independently and at a constant rate, which
may not always be the case. Understanding these limitations is
crucial for accurate application, especially in fields where While the
Poisson Distribution is powerful, it has limitations. It assumes
events occur independently and at a constant rate, which may not
always be the case. Understanding these limitations is crucial for
accurate application, especially in fields where event correlation
exists.

7. Conclusion
• The Poisson distribution is a powerful tool for modeling the
occurrence of events in a fixed interval.
• Its applications are vast, ranging from telecommunications to
healthcare and beyond.
• Mastery of this distribution can provide valuable insights into
predicting and managing real-world phenomena.