In my work I have come across a situation where I need to derive values from values having confidence intervalls. I want to calculate the confidence intervals for my derived values. I am quite rusty when it comes to performing math but I seem to recall there being some strange rules for doing these kind of operations and I seem to recall it not being so easy. Perhaps someone can shed some light on it for me...
Here is my problem (I have simplified the variable names a bit):
I have 5 variables $a$, $b$, $c$, $d$, and $e$ with confidence intervals $a_{lower}$, $a_{upper}$, $b_{lower}$, $b_{upper}$, $c_{lower}$, $c_{upper}$, $d_{lower}$, $d_{upper}$, $e_{lower}$, $e_{upper}$.
I then have the following derived values that I want to calculate confidence intervals for:
$$A=10^{a}$$ $$B=b$$ $$C=\frac{1}{10^c+1}$$ $$D=10^d$$ $$E=e$$ $$F=\frac{A\times C\times15\,000}{A\times C+15\,000}$$ $$G=\frac{E\times B\times 15\,000}{A\times C + 15\,000}$$ $$H=866\times\frac{D}{F}$$
Now, I am pretty sure that $A$ to $E$ is trivial, just plug the respective $?_{upper}$ and $?_{lower}$ values into the equation and be done but what about $F$ $G$ and $H$?