Random Variables

Abstract

The number of heads in a sequence of 10000 coin tosses, the number of days it takes until the next rain and the size of a genealogical tree are random numbers. All are functions of the outcome of a random experiment (performed either by man or by nature) and taking discrete values, that is, values in a countable set. These values are integers in the above examples, but they can be more complex mathematical objects, such as graphs for instance. This chapter gives the elementary rules for computing expectations, a list of famous discrete random variables or vectors (binomial, geometric, Poisson and multinomial), and the elementary theory of conditional expectation.