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## Main Question or Discussion Point

May I ask how to find the [tex]E\left(ln x\right)[/tex] and [tex]Var\left(ln x)[/tex]?

The [tex]X_{i}[/tex] are random sample from the [tex]f\left(x; \theta\right) = \theta x^{\theta - 1}I_{\left(0, 1\right)}\left(x\right)[/tex] where [tex]\theta > 0[/tex].

I need the information in finally solving the Cramer-Rao lower bound for the variance of an unbiased estimator of a function of [tex]\theta[/tex]. And also for checking if I have an unbiased estimator.

The [tex]X_{i}[/tex] are random sample from the [tex]f\left(x; \theta\right) = \theta x^{\theta - 1}I_{\left(0, 1\right)}\left(x\right)[/tex] where [tex]\theta > 0[/tex].

I need the information in finally solving the Cramer-Rao lower bound for the variance of an unbiased estimator of a function of [tex]\theta[/tex]. And also for checking if I have an unbiased estimator.