Appendix A

Complements

A.1 Basic probabilistic notions

A.1.1 Discrete random variable, expectation, and generating function

A.1.1.1 General random variable and its law

A probability space b01-math-0001 will be considered throughout. In general, an r.v. with values in a measurable state space b01-math-0002 is a measurable function

equation

Then, for every measurable subset b01-math-0004 of b01-math-0005, it holds that

equation

The law of b01-math-0007 is the probability measure defined on b01-math-0008 by b01-math-0009 and, more concretely, for measurable subsets b01-math-0010, by

A.1.1.2 Random variable with ...

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