# Probability generating functions – Further Probability & Statistics Paper 4

Candidates should be able to:

• understand the concept of a probability generating function (PGF) and construct and use the PGF for given distributions (Including the discrete uniform, binomial, geometric and Poisson distributions.)
• use formulae for the mean and variance of a discrete random variable in terms of its PGF, and use these formulae to calculate the mean and variance of a given probability distribution
• use the result that the PGF of the sum of independent random variables is the product of the PGFs of those random variables.