A single function that encodes an entire discrete distribution. Differentiating it produces the mean and variance, and multiplying two of them handles sums.
Syllabus points covered
- Understand and use the probability generating function of a discrete random variable
- Find the mean and variance from a probability generating function
- Find the probability generating functions of standard distributions
- Use the generating function of the sum of independent random variables
Common mistakes
- Forgetting that G(1) must equal 1, which is a useful check.
- Using G′(1) as the variance rather than the mean.
- Adding generating functions for a sum of independent variables when they should be multiplied.
- Not differentiating twice, or forgetting the correction term, when computing the variance.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Practice worksheetComing soon
- Worksheet answersComing soon
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questions
- Mark scheme
- Step-by-step worked solutionsComing soon
Looking for whole papers by session? All Further Mathematics past papers