# R9-Probability-1

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2018-02-18 15:45

## Section 1

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

Definition of Event | specified set of outcomes. |

Definition of Probability | The probability of any event E is a number between 0 and 1 - 0 ≤ P(E) ≤ 1. The sum of the probabilities of any set of mutually exclusive and exhaustive events equals 1 |

subjective probability, | may adjust an empirical probability to account for perceptions of changing relationships |

priori probability/objective | more narrow range of well-defined problems, we can sometimes deduce probabilities by reasoning about the problem. |

unconditional probability, denoted P(A). Unconditional probability/marginal probability | is also frequently referred to as |

conditional probability, denoted P(A | B) | probability of A, given that B has occurred? |

joint probability, denoted P(AB) | “What is the probability of both A and B happening?” |

equation of conditional probability | P(A | B) = P(AB)/P(B), P(B) ≠ 0 |

equation of joint probability | P(AB) = P(A | B)P(B) |

A or B occurs, or both occur, | P(A or B) = P(A) + P(B) – P(AB) |

Two events A and B are independent | P(A | B) = P(A) or, equivalently, P(B | A) = P(B). |

When two events are independent, the joint probability of A and B | P(AB) = P(A)P(B) |

total probability rule. | unconditional probability of the event in terms of probabilities conditional on the scenarios. |

eqn for totla probability rule | P ( A ) = P ( A S ) + P ( A S C ) = P ( A | S ) P ( S ) + P ( A ∣ ∣ S C ) P ( S C ) |

## Section 2

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

Definition of Expected Value | The expected value of a random variable is the probability-weighted average of the possible outcomes of the random variable. For a random variable X, the expected value of X is denoted E(X). |

Definition of Variance | The variance of a random variable is the expected value (the probability-weighted average) of squared deviations from the random variable’s expected value |

Definition of Standard Deviation | Standard deviation is the positive square root of variance. |

conditional expected values. | The expected value of a random variable X given an event or scenario S is denoted E(X | S). |

Total Probability Rule for Expected Value. | E(X) = E(X | S)P(S) + E(X | SC)P(SC) |

conditional variances, | variance of EPS given a declining interest rate environment and the variance of EPS given a stable interest rate environment. |

main points about conditional variances | 1) that variance, like expected value, has a conditional counterpart to the unconditional concept and 2) that we can use conditional variance to assess risk given a particular scenario. |

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