AQA S3 — Question 6

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

\hfill \mbox{\textit{AQA S3  Q6}}
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