／var／logmarcus chiu

Binomial Distribution Special Cases - (Poisson Distribution and Normal Distribution)

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Binomial variables represent a special case of 𝑆𝑛 = 𝑋1 + … + 𝑋𝑁, where all 𝑋𝑖 have Bernoulli distribution with some parameter 𝑝

Special Cases

Approximating Binomial Distribution with Poisson Distribution
  • small 𝑝 allows to approximate Binomial distribution with Poisson (number of success)
  • large 𝑝 allows to approximate Binomial distribution with Poisson (number of failures)

Approximating Binomial Distribution with Normal Distribution
  • moderate values of 𝑝 (say, 0.05 ≤ p ≤ 0.95) and for large 𝑛 approximates Normal Distribution