If is Normally Distributed with Mean and Variance , then
a linear function of ,

(1) |

(2) |

which is of the standard form with

(3) |

(4) |

(5) |

(6) |

Setting this equal to

(7) |

(8) | |||

(9) |

Therefore, the Mean and Variance of the weighted sums of Random Variables are their weighted sums.

If are Independent and Normally Distributed with
Mean 0 and Variance , define

(10) |

(11) |

© 1996-9

1999-05-25