# Continuous random variables – Further Probability & Statistics Paper 4

Candidates should be able to:

• use a probability density function which may be defined piecewise
• use the general result $$E(g(X)) = \int f(x)g(x)dx$$ 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 $$Y = X^3$$.)