Poisson and Binomial both the distribution are used for defining discrete events.You can tell that Poisson distribution is a subset of Binomial distribution.
Binomial is the most preliminary distribution to encounter probability and statistical problems.
On the other hand when any event occurs with a fixed time interval and having a fixed average rate then it is Poisson distribution.
The Poisson distribution is characterised by a rate (over time or space) of an event occurring. In a binomial distribution the probability is that of a single event (outcome) occurring in a repeated set of trials.
If this is the only information that you have then you must use the Poisson distribution.
The Poisson distribution is discrete.
Because "n" is very large and "p" is very small. where "n'' indicates the fixed number of item. And ''p'' indicates the fixed number of probability from trial to trial.
discrete & continuous
Discrete
The binomial distribution is a discrete probability distribution. The number of possible outcomes depends on the number of possible successes in a given trial. For the Poisson distribution there are Infinitely many.
The Poisson distribution is characterised by a rate (over time or space) of an event occurring. In a binomial distribution the probability is that of a single event (outcome) occurring in a repeated set of trials.
The Poisson distribution is a limiting case of the binomial distribution when the number of trials is very large and the probability of success is very small. The Poisson distribution is used to model the number of occurrences of rare events in a fixed interval of time or space, while the binomial distribution is used to model the number of successful outcomes in a fixed number of trials.
For the binomial, it is independent trials and a constant probability of success in each trial.For the Poisson, it is that the probability of an event occurring in an interval (time or space) being constant and independent.
A poisson process is a non-deterministic process where events occur continuously and independently of each other. An example of a poisson process is the radioactive decay of radionuclides. A poisson distribution is a discrete probability distribution that represents the probability of events (having a poisson process) occurring in a certain period of time.
The Poisson distribution with parameter np will be a good approximation for the binomial distribution with parameters n and p when n is large and p is small. For more details See related link below
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Lulla diference
Assuming that "piossion" refers to Poisson, they are simply different probability distributions that are applicable in different situations.
The triangular, uniform, binomial, Poisson, geometric, exponential and Gaussian distributions are some that can be so defined. In fact, the Poisson and exponential need only the mean.
If this is the only information that you have then you must use the Poisson distribution.