The general formula for the variance of a random variable

which is a function of

uncorrelated random variables

is
![\begin{align*}\sigma_y^2 = \sum_{i = 1}^n \left[\frac{\partial y}{\partial x_i} \right] \sigma_i^2\end{align*} \begin{align*}\sigma_y^2 = \sum_{i = 1}^n \left[\frac{\partial y}{\partial x_i} \right] \sigma_i^2\end{align*}](../images/1250c216e241d03bfd4ddc878fd6339ea2a779d5.gif)
where

is the variance of the random variable

and the partial derivative in brackets is evaluated at

equal to the mean of

for all

. In this case,

, and

is replaced by

.

where

and

are the means of the measurements of

and

, respectively. Thus,

or


because the measurements are uncorrelated. Therefore,

Therefore, answer (C) is correct.