Example of Poisson Distribution

• Given circumstances of previous Binomial example, what is chance that Frank Nagy smiles exactly once in a given lecture:

• Solution: Again, we set each trial = a smile and we have 1,000 of them. Now Success = ``Frank Nagy smiled this smile in our given lecture'' and it is not very probable . So, n is large, p is small, but is reasonable.

• So, the Poisson approximation to the exact (in this example) Binomial distribution is valid and chance is , i.e., it is quite probable that Frank smiles once and once only in a given lecture.

• The binomial estimate is

  

  which is indeed .