SPS SPS FM Statistics 2026 January — Question 4

Exam BoardSPS
ModuleSPS FM Statistics (SPS FM Statistics)
Year2026
SessionJanuary
TopicPoisson Distribution
TypeExpectation and variance of Poisson-related expressions

4. The numbers of customers arriving at a ticket desk between 8 a.m. and 9 a.m. on a Monday morning and on a Tuesday morning are denoted by \(X\) and \(Y\) respectively. It is given that \(X \sim \operatorname { Po } ( 17 )\) and \(Y \sim \operatorname { Po } ( 14 )\).
  1. Find
    (a) \(\mathrm { P } ( X + Y ) > 40\),
    (b) \(\operatorname { Var } ( 2 X - Y )\).
  2. State a necessary assumption for your calculations in part (i) to be valid.
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