# R9-Probability-2

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## PORTFOLIO EXPECTED RETURN AND VARIANCE OF RETURN

Question | Answer | Column 3 |
---|---|---|

Properties of Expected Value | The expected value of a constant times a random variable equals the constant times the expected value of the random variable | E(wiRi) = wiE(Ri) |

Properties of Expected Value | The expected value of a weighted sum of random variables equals the weighted sum of the expected values, using the same weights | |

Calculation of Portfolio Expected Return. | Given a portfolio with n securities, the expected return on the portfolio is a weighted average of the expected returns on the component securities | E(Rp)= E(w1R1....wnRn) |

Definition of Covariance | Cov(Ri,Rj) = E[(Ri-ERi)(Rj-ERj)] | σ(Ri,Rj) and σij. |

interpret the sign of covariance as follows | negative | when the return on one asset is above its expected value, the return on the other asset tends to be below its expected value |

interpret the sign of covariance as follows | positive | returns on both assets tend to be on the same side (above or below) their expected values at the same time |

interpret the sign of covariance as follows | 0 | returns on the assets are unrelated |

The covariance of a random variable with itself (own covariance) is its own variance | Cov(R,R) = E{[R − E(R)][R − E(R)]} = E{[R − E(R)]2} | σ2(R) |

Definition of Correlation | ρ(Ri,Rj) = Cov(Ri,Rj)/σ(Ri)σ(Rj). Alternative notations are Corr(Ri,Rj) and ρij. | |

Properties of Correlation | A correlation of 0 (uncorrelated variables) indicates an absence of any linear (straight-line) relationship between the variables.13 Increasingly positive correlation indicates an increasingly strong positive linear relationship (up to 1, which indicates a perfect linear relationship). Increasingly negative correlation indicates an increasingly strong negative (inverse) linear relationship (down to −1, which indicates a perfect inverse linear relationship) | |

joint probability function of two random variables X and Y, denoted P(X,Y) | gives the probability of joint occurrences of values of X and Y. For example, P(3, 2), is the probability that X equals 3 and Y equals 2 | |

Definition of Independence for Random Variables | Two random variables X and Y are independent if and only if P(X,Y) = P(X)P(Y). | |

Multiplication Rule for Expected Value of the Product of Uncorrelated Random Variables | The expected value of the product of uncorrelated random variables is the product of their expected values. | |

## TOPICS IN PROBABILITY

Question | Answer | Column 3 | |
---|---|---|---|

Bayes’ Formula | Bayes’ formula is a rational method for adjusting our viewpoints as we confront new information.17 Bayes’ formula and related concepts have been applied in many business and investment decision-making contexts, including the evaluation of mutual fund performance | P( Event| Information ) = P (Information| Event) P (Information) P(Event) | |

Principles of Counting | If one task can be done in n1 ways, and a second task, given the first, can be done in n2 ways, and a third task, given the first two tasks, can be done in n3 ways, and so on for k tasks, then the number of ways the k tasks can be done is (n1)(n2)(n3) … (nk). | Multiplication rule | |

Principles of Counting | Multinomial Formula (General Formula for Labeling Problems) | The number of ways that n objects can be labeled with k different labels, with n1 of the first type, n2 of the second type, and so on, with n1 + n2 + … + nk = n | n!/(n1!.n2!.....nk!) |

Principles of Counting | Combination Formula (Binomial Formula) | The number of ways that we can choose r objects from a total of n objects, when the order in which the r objects are listed does not matter, is | look up formula |

Principles of Counting | Permutation Formula | nPr | |

United States | Washington DC | ||

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