A variable that can take any value in a range, described by a density function. Probability becomes area, and sums become integrals.
Syllabus points covered
- Use a probability density function to find probabilities, mean and variance
- Find and use the cumulative distribution function
- Find the median, quartiles and other percentiles of a continuous distribution
- Find the distribution of a function of a continuous random variable
Common mistakes
- Integrating over the wrong interval, or over regions where the density is zero.
- Forgetting that the total area under the density function must be 1.
- Using E(X²) as the variance without subtracting the square of the mean.
- Confusing the density function with the cumulative distribution function when finding the median.
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
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