Asset-Liability and Liquidity Management

Appendix: Elements of Probability and Statistics

In this Appendix we provide a brief overview of some statistical concepts that are needed for a better understanding of the materials discussed in the body of the text.

RANDOM VARIABLES

The set of all possible outcomes of an experiment is called the sample space of that experiment. For example, in rolling a fair six-sided die, the sample space is . A random variable is a real-valued function defined on the sample space that associates each outcome of an experiment to a real number. The state space is all possible real values that a random variable can assume. Therefore, random variable is a function from sample space to state space where members of the sample space are all possible outcomes of the experiment and members of state space are all possible values that the random variable can assume. For example, in an experiment in which a fair die is rolled four times, the sample space consists of all possible sequences of numbers that ...