Given sets of variates denoted , ..., , a quantity called the Covariance Matrix is defined
by

(1) | |||

(2) | |||

(3) |

where and are the Means of and , respectively. An individual element of the Covariance Matrix is called the covariance of the two variates and , and provides a measure of how strongly correlated these variables are. In fact, the derived quantity

(4) |

(5) |

(6) |

(7) |

For two independent variates and ,

(8) |

The covariance obeys the identity

(9) |

By induction, it therefore follows that

(10) | |||

(11) | |||

(12) | |||

(13) | |||

(14) |

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1999-05-25