If I have a monotonic function, say ln, can I bring it inside an integral?
in other words, is $$\ln\left[ \int f(x)\, dx\right] = \int \ln(f(x))\, dx.$$
My limits of integration don't depend on $x,$ so I think I can.
Could I move expectation inside the integral?
(I am working on something with the Cramer-Rao inequality, which requires that I take the natural log and then the expectation of a function.)