Notes on Probability Theory
نویسنده
چکیده
I Axioms of Probability 2 I-A Set Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 I-A1 Set Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 I-A1a Subsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 I-A1b Mutually Exclusive Sets or Disjoint Sets . . . . . . . . . . . . . . . . . . . 2 I-A2 Partitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 I-A3 Complements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 I-B Probability Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 I-B1 The Axioms of Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 I-B2 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 I-B3 Von Mises and the Frequency Interpretation . . . . . . . . . . . . . . . . . . 3 I-B4 Equality of Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 I-B5 The class F of events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 I-B5a Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 I-B6 Axiomatic Definition of an Experiment . . . . . . . . . . . . . . . . . . . . . 4 I-B6a Countable Spaces: Case when I consists of N countable outcomes. . . . 4 I-B6b Non-countable Spaces: The real line . . . . . . . . . . . . . . . . . . . . . 4 I-C Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 I-C1 Total Probability and Bayes’ Theorem . . . . . . . . . . . . . . . . . . . . . . 5 I-C2 Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
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