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]