# Is the confidence interval of f(x) equal to f( confidence interval(x))?

The problem is that I can only observe $X$ and calculate $f(X)$ analytically so I need to compute the confidence interval of $f(X)$ via $X$.

-

Only if $f$ is monotonic. Then the probability of the interval is preserved.

-
Thank you very much! –  user49300 Nov 13 '12 at 23:57