Statistics 简明教程
Statistics - Poisson Distribution
泊松输送是离散的可能性色散，在可测量的工程中广泛应用。这种输送是由法国数学家西蒙·丹尼·泊松博士于 1837 年产生的，色散以他的名字命名。泊松循环用在那些情况下，即情景发生可能性小，即情景偶尔发生。比如，在组装组织中出错的事情的可能性小，一年中发生震颤的可能性小，街道上的事故可能性小，等等。这些都是情景可能性小的事件的案例。
Poisson conveyance is discrete likelihood dispersion and it is broadly use in measurable work. This conveyance was produced by a French Mathematician Dr. Simon Denis Poisson in 1837 and the dissemination is named after him. The Poisson circulation is utilized as a part of those circumstances where the happening’s likelihood of an occasion is little, i.e., the occasion once in a while happens. For instance, the likelihood of faulty things in an assembling organization is little, the likelihood of happening tremor in a year is little, the mischance’s likelihood on a street is little, and so forth. All these are cases of such occasions where the likelihood of event is little.
泊松分布通过以下概率函数定义和给出：
Poisson distribution is defined and given by the following probability function:
Formula
其中——
Where −
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${m}$ = Probability of success.
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${P(X-x)}$ = Probability of x successes.
Example
Problem Statement:
Problem Statement:
一个别针生产商意识到，通常情况下，他生产的物品中有 5% 是有缺陷的。他在 100 个一包的包裹内提供别针，并保证不超过 4 个别针会有缺陷。一包别针符合保证质量的可能性是多少？[给定：${e^{-m}} = 0.0067$]
A producer of pins realized that on a normal 5% of his item is faulty. He offers pins in a parcel of 100 and insurances that not more than 4 pins will be flawed. What is the likelihood that a bundle will meet the ensured quality? [Given: ${e^{-m}} = 0.0067$]
Solution:
Solution:
设 p = 有缺陷别针的概率 = 5% = $\frac{5}{100}$。我们给定：
Let p = probability of a defective pin = 5% = $\frac{5}{100}$. We are given:
泊松分布给出为：
The Poisson distribution is given as:
所需概率 = P [一包别针将满足保证]
Required probability = P [packet will meet the guarantee]