AQA S3 2006 June — Question 6

Exam BoardAQA
ModuleS3 (Statistics 3)
Year2006
SessionJune
TopicPoisson Distribution
TypeProving Poisson properties from first principles
6 The random variable \(X\) has a Poisson distribution with parameter \(\lambda\).
  1. Prove that \(\mathrm { E } ( X ) = \lambda\).
  2. By first proving that \(\mathrm { E } ( X ( X - 1 ) ) = \lambda ^ { 2 }\), or otherwise, prove that \(\operatorname { Var } ( X ) = \lambda\).
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