CAIE A-Level Mathematics 6.1.1 Poisson Probabilities

CAIE A-Level Mathematics 6.1.1 Poisson Probabilities
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise rescaling a Poisson mean for a changed interval and evaluating exact, ranged or tail probabilities with e^−λ λ^r/r!, finite sums and complements.

How this is tested

  • scale λ by the ratio of the requested interval, area or population to the stated one
  • substitute r into e^−λ λ^r/r! for an exact number of randomly occurring events
  • sum the required integer terms or subtract an unwanted lower tail from one

Question 1(a)

[Maximum number: 2]

The random variables X and Y have independent distributions X∼Po⁡(3)X \sim \operatorname{Po}(3) and Y∼Po⁡(2)Y \sim \operatorname{Po}(2) respectively.

Find P(2<X<5).