The expectation E(r)=np of binomial distribution, the variance Var(r)=npq, and the expectation sum variance of Poisson distribution is λ. At this time, we need the expectation and variance of these two distributions to be similar, that is, np and npq are approximately equal.

It can be seen from the above that when n of binomial distribution is large and p is small, Poisson distribution can be used as an approximation of binomial distribution, where λ is np. Usually, when n≥20 and p≤0.05, Poisson formula can be used for approximate calculation.

Application of Poisson Distribution Formula

The exponential distribution refers to the time interval between two events. Different from Poisson distribution, Poisson distribution is discrete and exponential distribution is continuous. If the number of events per unit time satisfies Poisson distribution, then the time interval of events satisfies exponential distribution.

This little game * * * consists of four topics, so what if this little game has 100 topics or even 1000 topics? Just calculating the combination formula can make you count to the top. In fact, in this case, Poisson distribution can also help. So let's review the expectation and variance of binomial distribution first.

Poisson distribution is suitable for describing the probability distribution of the number of random events per unit time. For example, the number of service requests received by a service facility in a certain period of time, the number of calls received by telephone exchanges, the number of guests waiting at car platforms, the number of machine failures, the number of natural disasters, the variation of DNA sequences, the decay of radioactive nuclei, the photon number distribution of lasers and so on.