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Chapter 1

RS Chapter 1 Random Variables6/14/20191 Chapter 1 Probability Theory: IntroductionBasic Probability General In a probability space ( , , P), the set is the set of all possible outcomesof a probability experiment . Mathematically, is just a set, with elements . It is called the sample space. An eventis the answer to a Yes/No question. Equivalently, an event is a subset of the probability space: A . Think of A as the set of outcomes where the answer is Yes , and Acis the complementary set where the answer is No . A -algebra is a mathematical model of a state of partial knowledge about the outcome.

A sigma-algebra (σ-algebra or σ-field) F is a set of subsets ωof Ωs.t.: F. ... notation P, and the measure space is a probability space. Measures & Measure Space. RS – Chapter 1 – Random Variables 6/14/2019 7 • There is a unique measure λon (R, BR) that satisfies

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