# Why doesn't the Cramer-Rao lower bound apply?

Let $X_1, X_2, \dots, X_n$ be a sample of i.i.d. random variables, with density $$f_\theta=\frac{2}{3\theta}\left(1-\frac{x}{3\theta}\right)$$ for $0 < x < 3\theta$. And $f_\theta=0$ if $x < 0$ or $x>3\theta$

Let $\hat{\theta}=\overline{X}$ be an estimate for $\theta$

I showed that $\hat\theta$ is an unbiased estimator for $\theta$ and it's a consistent estimator.

My question is:

Why doesn't the Cramer-Rao lower bound apply to unbiased estimates of for this distribution?

Are you aware of the three regularity conditions that must be satisfied for the CR lower bound to apply? It looks like it violates the condition that the bounds of the distribution function must not depend upon the quantity being estimated. $\theta$ determines the bounds of the distribution. See the Wikipedia article, regularity condition 1: http://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93Rao_bound