Let me give an example. What is the Poisson distribution and the exponential distribution? I am afraid most people can’t say it clearly.
I can let you understand these two concepts effortlessly in 10 minutes.
In daily life, a large number of events have a fixed frequency.
An average of 3 babies per hour in a hospital
A company receives an average of 1 call every 10 minutes.
A supermarket sells an average of 4 packs of xx brand milk powder per day.
A website has an average of 2 visits per minute
They are characterized by the fact that we can estimate the total number of these events, but we cannot know the exact time of occurrence. It is known that an average of 3 babies are born every hour. How many children will be born in the next hour?
It is possible to have six births at a time, or one may not be born. This is something we can't know.
The Poisson distribution is the specific probability of occurrence of an event during a certain period of time.
Above is the formula for the Poisson distribution. On the left side of the equal sign, P is the probability, N is a certain functional relationship, t is the time, n is the number, and the probability of birth of 3 babies in 1 hour is expressed as P(N(1) = 3). On the right side of the equal sign, λ indicates the frequency of the event.
For the next two hours, the probability that a baby will not be born is 0.25%, which is almost impossible.
In the next hour, the probability of having at least two babies born is 80%.
The pattern of the Poisson distribution is roughly the same as below.
It can be seen that in the vicinity of the frequency, the probability of occurrence of the event is the highest, and then the symmetry decreases toward both sides, that is, it becomes unlikely to be larger and smaller. It is the most likely outcome to have 3 babies born per hour. The more or less born, the less likely it is.
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