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A.G · 2021年10月15日

辅导员，这里也是没明白为啥要接近于1

  1. FRM I
  2. Quantitative

NO.PZ2016062402000016

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.

辅导员，这里也是没明白为啥要接近于1，数据的规模这个是没有问题

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1 个答案

品职答疑小助手雍 · 2021年10月16日

同学你好，这道题是2004年前的真题了。我们最近查了下原版书和notes，上面并没有这道题的结论。在泊松分布中，λ的定义是单位时间内事件的发生率（发生个数）。我们推测，之所以在04年时这道题选λ最大为1，是当时FRM参考书的定义问题。但我们现在都不这样说了，因为单位时间内事件发生的个数是可以大于1的。并且，我记得之前学概率论的时候，只是强调泊松分布中，λ=np的n足够大，就可以由中心极限定理趋近于正态分布。

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