(14.24) | |||

Cov | (14.25) | ||

(14.26) | |||

(14.27) |

To verify the results let us consider two independent measurements and ; let us calculate the correlated quantities and , and finally their product ( ) and their ratio ( ):

(14.28) | |||

(14.29) |

It follows that

(14.30) | |||

(14.31) |

Just as an unknown common offset error cancels in differences and is enhanced in sums, an unknown normalization error has a similar effect on the ratio and the product. It is also interesting to calculate the standard uncertainty of a difference in the case of a normalization error:

(14.32) |

The contribution from an unknown normalization error vanishes if the two values are equal.