There are two principal methods used to generate random numbers. There are a number of inequalities involving the expected values of functions of random variables. Let be the sum of random variables. Probability generating functions are particularly useful for dealing with functions of independent random variables. The game consists of a sequence of challenges played in a random order. These are selected by a combination of computer analysis of return information and random sampling. Often the i.i.d. assumption arises in the context of sequences of random variables. Another important application is to the theory of the decomposability of random variables. These materials are used to create items with random bonuses. Characteristic functions are particularly useful for dealing with linear functions of independent random variables. Shuffling is the process of bringing the cards of a pack into a random order. A similar notion exists for collections of random variables. Dice rolls are provided by random or pseudorandom number generators. Copulas are used to describe the dependence between random variables. Covariance is a measure of linear relationship between the random variables.