# Confidence interval of two variances

I have two normally distributed samples $[x_1, x_2, \ldots, x_n]$ with sample variance $s^2_1$ and another sample $[y_1, y_2,\ldots, y_n]$ with sample variance $s^2_2$.

I know how to calculate the confidence interval for each of the variances. However i do not know how to calculate the confidence interval of the sum of the two variances.

In other words, can someone help me to calculate the confidence interval for $\sigma^2_1+\sigma^2_2$.

• This is a standard problem covered in statistics textbooks. Did you try consulting them first? You can ask then what in particular your did not understand. – mpiktas Mar 18 '14 at 8:50
• Hi mpiktas, Thx. I never studied statistics so i am not familiar with stat books. However, generally if something is in the book it is typically available in Google, but I failed to find anything in Google. If you know the solution can u post it here and give me a link ... – user42131 Mar 18 '14 at 8:54
• Are $X$ and $Y$ independent? If so, what is the variance of $Z=X+Y$? – soakley Mar 19 '14 at 0:07
• hi soakley. Yes X and Y are independent: I assume you suggest to define Z=X+Y with var(Z)=var(X)+var(Y). Can I now assume that Z is normally distributed and use the sample Z and apply the same technique to estimate the confidence interval for var(Z)? – user42131 Mar 19 '14 at 9:10
• is there any statistics guru here who can answer to my question? Some claim this to be a trivial problem, but i asked even some statistics graduate, but it si not a trivial problem.... – user42131 Mar 25 '14 at 14:30