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CAIE A-Level Further Math AS 4.5 Probability Generating Functions Questions

Practise constructing PGFs, extracting probabilities, differentiating for moments and combining independent variables.

Syllabus
2028–2030
Course
Further Mathematics 9231
Level
AS

Exam points

  • construct G_X(t)=ΣP(X=x)t^x from a probability table or discrete model
  • read probabilities from coefficients and use derivatives at t=1 for moments
  • multiply PGFs only when the summed random variables are independent

Covered syllabus points

4.5.1—Probability generating functions4.5.2—PGF mean and variance4.5.3—Sums of random variables

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