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21 SOME PROBABILITY TECHNIQUES

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(a) | Symbols used in symbolic logic |

(b) | Simple probability notations |

(c) | Special values of p |

(d) | Relationship of events |

(e) | The laws of probability |

(f) | Some theorems (including Bayes' theorem) |

(g) | The deciban |

(h) | Methods of applying the above axioms |

(i) | Theorem of the weighted average of factors |

(j) | Theorem of the chain of witnesses |

(k) | Expected value, standard deviation, variance, distributions |

(l) | Some special distributions |

(m) |
Some simple formulae of a non-analytic type, concerning proportional bulges |

(n) | The general formula for sigma in Tunny work |

(o) | The statistician's fallacy |

(p) | The principle of maximum likelihood |

It is assumed that the reader has at any rate an elementary knowledge of probability theory. Therefore the account presented here does not contain many examples but is mainly a list of definitions, notations and theorems. Rigour is __deliberately__ avoided when it would make the account more difficult to read.

(a) __Symbols used in symbolic logic__.

∨ means 'or'

**.** means 'and', but the symbol **.** is often omitted, thus E**.**F can be written EF (E and F being propositions).

~ means 'not', but we shall write '' instead of the usual '~X'.

(b) __Simple probability notations__.

P(E|H) means the probability of an event E given a hypothesis H. When H is taken for granted we write P(E) simply.

The letter p represents a probability.

The letter o represents odds and is defined by the equation

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