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Threshold for mean = variance in Poisson distribution

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

  1. 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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