Find the Rao-Cramer inequality if the random sample 1,2,..., is taken from the distribution with the p.d.f.
$$ f(x;)= e^{-(x-)}$$
where $>$
I am aware of that I need to calculate:
$$ \frac{1}{-n[\frac{d^2}{dθ^2}ln(f(x;θ))]} or \frac{1}{-n[\frac{d}{dθ}ln(f(x;θ))]^2} $$
I calculated log-likelihood as:
$$ lnL = lne^{-θn} + lne^{\sum_{i=1}^n x_i} = -θn + \sum_{i=1}^n x_i$$ $$ \frac{dlnL}{dθ} = -n $$ $$ \frac{d^2lnL}{dθ^2} = -1 $$
Is there a problem with calculations? How can I calculate the lower bound?