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薛真 · 2020年02月23日

问一道题：NO.PZ2016062402000016

  1. FRM I
  2. Quantitative

问题如下：

When can you use the normal distribution to approximate the Poisson distribution, assuming you have n independent trials, each with a probability of success of p?

选项：

A.

When the mean of the Poisson distribution is very small

B.

When the variance of the Poisson distribution is very small

C.

When the number of observations is very large and the success rate is close to 1

D.

When the number of observations is very large and the success rate is close to 0

解释：

The normal approximation to the Poisson improves when the success rate, χ, is very high. Because this is also the mean and variance, answers A and B. are wrong. In turn, the binomial density is well approximated by the Poisson density when np = χ is large.

为啥不选D，possion分布的适用条件不是概率很小，N很大吗？老师讲的

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1 个答案

品职答疑小助手雍 · 2020年02月24日

同学你好，它这里对success rate的定义是λ，而不是p。泊松分布中，λ=np的n足够大，就可以由中心极限定理趋近于正态分布。

可以参考讲义84页。

薛真 · 2020年02月24日

那这个题λ是平均值，N是试验次数，什么是p呢

品职答疑小助手雍 · 2020年02月24日

p是单次成功的概率，如果实在不理解的话可以去看一下基础班关于二项分布和泊松分布的那一部分。

薛真 · 2020年02月28日

题目中并没有说他是单词成功的概率还是平均的概率啊

品职答疑小助手雍 · 2020年02月28日

题目说了 each with

薛真 · 2020年02月29日

对啊，每一个成功的概率是P,并非平均值啊

品职答疑小助手雍 · 2020年02月29日

每个概率都是p，为什么平均每个成功的概率不是p？

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