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Further Probability & Statistics — 9231 FPS

Each skill has notes, three worked examples, two original written problems and eight short checks, including fresh review variants. Recent exam practice uses questions dated 2020–2026.

All course resources · Examination questions, 2020–2026

Before you start Further Statistics

Build on Statistics 1 and 2: probability models, normal and Poisson distributions, sampling, confidence intervals and hypothesis tests.

Statistics bridge: twelve prerequisite topics · Review Statistics 1 · Review Statistics 2

Continuous random variables

The probability density function · Check answers
The cumulative distribution function · Check answers
Calculating E(g(X)) for a continuous random variable · Check answers
Finding the probability density function and cumulative distribution function of Y = g(X) · Check answers
End-of-chapter review exercise 8 · Check answers

Inferential statistics

t-distribution · Check answers
Hypothesis tests concerning the difference in means · Check answers
Paired t-tests · Check answers
Confidence intervals for the mean of a small sample · Check answers
Confidence intervals for the difference in means · Check answers
End-of-chapter review exercise 9 · Check answers

Chi-squared tests

Forming hypotheses · Check answers
Goodness of fit for discrete distributions · Check answers
Goodness of fit for continuous distributions · Check answers
Testing association through contingency tables · Check answers
End-of-chapter review exercise 10 · Check answers

Non-parametric tests

Non-parametric tests · Check answers
Single-sample sign test · Check answers
Single-sample Wilcoxon signed-rank test · Check answers
Paired-sample sign test · Check answers
Wilcoxon matched-pairs signed-rank test · Check answers
Wilcoxon rank-sum test · Check answers
End-of-chapter review exercise 11 · Check answers

Probability generating functions

The probability generating function · Check answers
Mean (E(X)) and variance (Var(X)) using the probability generating function · Check answers
The sum of independent random variables · Check answers
Three or more random variables · Check answers
End-of-chapter review exercise 12 · Check answers
Cross-topic review exercise 2 · Check answers