CAIE S2 2020 June — Question 4

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2020
SessionJune
PaperDownload PDF ↗
TopicPoisson Distribution
4 The random variable \(A\) has the distribution \(\operatorname { Po } ( 1.5 ) . A _ { 1 }\) and \(A _ { 2 }\) are independent values of \(A\).
  1. Find \(\mathrm { P } \left( A _ { 1 } + A _ { 2 } < 2 \right)\).
  2. Given that \(A _ { 1 } + A _ { 2 } < 2\), find \(\mathrm { P } \left( A _ { 1 } = 1 \right)\).
  3. Give a reason why \(A _ { 1 } - A _ { 2 }\) cannot have a Poisson distribution.
4 The random variable $A$ has the distribution $\operatorname { Po } ( 1.5 ) . A _ { 1 }$ and $A _ { 2 }$ are independent values of $A$.\\
(a) Find $\mathrm { P } \left( A _ { 1 } + A _ { 2 } < 2 \right)$.\\

(b) Given that $A _ { 1 } + A _ { 2 } < 2$, find $\mathrm { P } \left( A _ { 1 } = 1 \right)$.\\

(c) Give a reason why $A _ { 1 } - A _ { 2 }$ cannot have a Poisson distribution.\\

\hfill \mbox{\textit{CAIE S2 2020 Q4}}
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