Confidence interval for fuction of random variables

I am struggeling with the following problem: Let A, B, C be normally distributed random variables, the means and variances are not known. Assume further that we have a sample of each of the distributions of A, B, C. With these samples one could calculate a confidence interval for the mean for each of the three random variables A, B, C (for example using Student's t-distribution), for e.g. alpha=0.05.
Now consider the following quantity with the (true) means mean(A), mean(B), mean(C) of the distributions of the random variables A, B, C:
m= (mean(A) + mean(B) + mean(C))/3,
v = 3 * \sqrt{(m-mean(A))^2 + (m-mean(B))^2 + (m-mean(C))^2} / (2 * m) (the variation coefficient of the sample mean(A), mean(B), mean(C)).

How can one calculate a confidence interval for v, given the confidence intervals for mean(A), mean(B), mean(C)?

It would be great if anyone had an idea or hints for literature. Thanks!


Active Member
So long as the samples are not to small, margin of error MOE(A+B+C)/3) = (sqrt(MOE(A)^2+MOE(B)^2+MOE(B)^2))/3 and you can get the MOEs from the CIs.