Bayesian Statistics: An Introduction, 4th Edition

1.3 Random variables

1.3.1 Discrete random variables

As explained in Section 1.1, there is usually a set Ω representing the possibilities consistent with the sum total of data available to the individual or individuals concerned. Now suppose that with each elementary event ω in Ω, there is an integer which may be positive, negative or zero. In the jargon of mathematics, we have a function mapping Ω to the set of all (signed) integers. We refer to the function as a random variable or an r.v.

A case arising in the context of the very first example we discussed, which was about tossing a red die and a blue die, is the integer representing the sum of the spots showing. In this case, ω might be ‘red three, blue two’ and then would be 5. Another case arising in the context of the second (political) example is the Labour majority (represented as a negative integer should the Conservatives happen to win), and here ω might be ‘Labour 350, Conservative 250’ in which case would be 100.

Rather ...