Let $X_{1}, \ldots, X_{n}$ be independent rvs with mean values $\mu_{1}, \ldots, \mu_{n}$ and variances $\sigma_{1}^{2}, \ldots, \sigma_{n}^{2}$ . Consider a function $h\left(x_{1}, \ldots, x_{n}\right),$ and use it to define a new rv $Y=h\left(X_{1}, \ldots, X_{n}\right) .$ Under rather general conditions on the $h$ function, if the $\sigma_{i}$ s are all small relative to the corresponding $\mu_{i} \mathrm{s},$ it can be shown that $E(Y) \approx h\left(\mu_{1}, \ldots, \mu_{n}\right)$ and

$\operatorname{Var}(Y) \approx\left(\frac{\partial h}{\partial x_{1}}\right)^{2} \cdot \sigma_{1}^{2}+\cdots+\left(\frac{\partial h}{\partial x_{n}}\right)^{2} \cdot \sigma_{n}^{2}$

where each partial derivative is evaluated at $\left(x_{1}, \ldots, x_{n}\right)=\left(\mu_{1}, \ldots, \mu_{n}\right) .$ Suppose three resistors

with resistances $X_{1}, X_{2}, X_{3}$ are connected in parallel across a battery with voltage $X_{4}$ . Then by Ohm's law, the current is

$Y=X_{4}\left(\frac{1}{X_{1}}+\frac{1}{X_{2}}+\frac{1}{X_{3}}\right)$

Let $\mu_{1}=10 \Omega, \sigma_{1}=1.0 \Omega, \mu_{2}=15 \Omega, \sigma_{2}=1.0 \Omega, \mu_{3}=20 \Omega, \sigma_{3}=1.5 \Omega, \mu_{4}=120 \mathrm{V}$

$\sigma_{4}=4.0 \mathrm{V} .$ Calculate the approximate expected value and standard deviation of the current (suggested by "Random Samplings," CHEMTECH, $1984 : 696-697 )$