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Threshold for mean = variance in Poisson distribution

Discussion in 'Mathematics' started by astromouse, Jul 15, 2011.

  1. astromouse

    astromouse New commenter

    My further maths students came across an exam question that required the poisson distribuiton to be a model (S2, AQA). The mean and variance varied more than they expected (by maybe 10%). How 'equal' do they have to be? Is there a threshold? (1%?)
  2. The OCR S2 syllabus requires students to know that the Poisson can be used as an approximation to the binomial if n > 50 and np < 5, approximately. So at the limit n=50 p=0.1 q=0.9 gives a mean of 5 and variance of 4.5. So a difference of up to 10% would seem reasonable.<font size="3" face="Times New Roman"></font>

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