# QM 3 ( Reading 8, Probabilities )

rename
lightenning's
version from
2017-03-22 17:00

## Section

Question | Answer |
---|---|

Outcome | The observed value of a random variable |

Event | Could be a single outcome, or a set of outcomes |

Exhaustive events | Events that cover all possible outcomes for an event |

Methods of Estimating probabilities | Empirical, Subjective, Priori |

Empirical probability | Estimates the probability of an event based on the frequency of its occurance in the past |

Subjective probability | Draws on subjective reasoning and personal judgment to estimate probabilities |

Priori Probability | based on formal analysis and reasoning rather than personal judgement. |

Dutch Book Theorem | if Probabilities reflected in the stock prices are not consistent, they give rise to profit opportunities until it is resolved |

Unconditional Probability | Probability whose occurence does not rely on another happening and is a stand alone probability |

Conditional Probability ( P(A|B) ) | Probability of an event occurring given that another event has happened. |

Joint probability | Probability of both A and B happening (P (AB) ). if A and B are mutually exclusive, both of them cannot happen at the same time and hence, P(AB)=0 |

P(A|B) formula | P(A|B)= P(AB)/P(B) ===> P(AB) = P(A|B) x P(B) |

P(A or B) formula | P ( A or B ) = P(A) + P(B) - P(AB) |

Dependent event | Events whose occurrence depends on other events |

independent event | events whose occurrence does not depend on another event. |

P(A|B) for independent events | P(A|B)= P(A) & P(B|A) = P(B) |

P(A and B) for independent events | = P(A) x P(B) |

Total probability rule | Express the unconditional probability of an event in terms of conditional probabilities for mutually exclusive and exhaustive events. |

Total probability Formula | P(A) = P(A|S1) x P(S1) + P(A|S2) x P(S2) +...+ P(A|Sn) x P(Sn) |

Expected Value | Probability weighted average of all possible outcomes |

Expected value Formula | E(X) = Sigma P(X)Xi ==> for a dice, its 1/6 x 1 + 1/6x2 + 1/6x3 + ... |

Variance of X | E{[X-E(X)]^2} |

Variance of X | Sigma P(Xi)[Xi - E(X)]^2\ |

Unconditional Value based on Conditional values | E(X) = E (X|S)P(S) + E (X|S^)P(S^) |

Unconditional Value based on Conditional values | E(X) = E (X|S1)P(S1) + E (X|S2)P(S2) + .... + E (X|Sn) P(Sn) |

## Pages linking here (main versions and versions by same user)

No other pages link to this page. See Linking Quickstart for more info.