(6.35) | |||

Cov | (6.36) | ||

(6.37) | |||

(6.38) |

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 ( ):

(6.39) | |||

(6.40) |

It follows that

(6.41) | |||

(6.42) |

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:

(6.43) |

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