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FRM Part I · FRM Exam Part I · Common Univariate Random Variables

Which statement about approximating a binomial distribution with a Poisson distribution is most appropriate?

The Poisson approximation works well when the number of trials is large and the success probability is small, with lambda set equal to np. In this case the binomial variance np(1-p) is close to its mean, matching the Poisson property.

  1. AIt works well when n is large and p is small, using lambda = npCorrect
  2. BIt works well when p is near 0.5 and n is small, using lambda = p
  3. CIt is exact whenever the trials are independent, regardless of n and p
  4. DIt requires the Poisson variance to differ from its mean by a factor of (1-p)

Explanation

For large n and small p, the binomial is well approximated by a Poisson with lambda = np, since variance np(1-p) is close to np. It is not exact, and small n with p near 0.5 is a poor case.

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