Suppose that $X_1,...,X_n$ is a random sample from a distribution with pdf :
$$ f(x,\theta)= \frac{\theta^3}{2}x^2e^{-\theta x} \space for \space 0,x,\infty$$
I found that $l(\theta)=-nlog(2)+3nlog(\theta) +2\sum X_i -\theta \sum X_i$
Then $\frac{d^2}{d\theta^2}=\frac{-3n}{\theta^2}$ therefore fisher information $I(\theta)= \frac{3n}{\theta^2}$
How can i derive the asymptotic distribution from here ?