A-Level Further Statistics – Continuous Random Variable PPT and Lesson Booklet

Use a probability density function which may be defined piecewise

Use the general result E(g(x)) =∫f(x)g(x) dx where f(x) is the probability density function of the continuous random variable X and g(X) is a function of X

Understand and use the relationship between the probability density function (PDF) and the cumulative distribution function (CDF), and use either to evaluate probabilities or percentiles

Use cumulative distribution functions (CDFs) of related variables in simple cases e.g. given the CDF of a variable X, find the CDF of a related variable Y, and hence its PDF, e.g. where Y = X^ 3.