#zettel #statistics-and-probability sourced from: [[Cramer-Rao Lower Bound]] # How to find the [[Cramer-Rao Lower Bound]] 1. Write the log likelihood function (LLF) as a function of $\theta$ - $\text{ln} \hspace{0.2em} p(\mathbf{x}; \theta)$ 2. Fix $\mathbf{x}$ and take the second partial of LLF: - $\partial^2 \text{ln} \hspace{0.2em} p(\mathbf{x}; \theta) / \partial \theta^2$ 3. If the result still depends on $\mathbf{x}$, - Fix $\theta$ and take [[Expected Value]] w.r.t. $\mathbf{x}$ - Otherwise skip this step. 4. The result may still depend on $\theta$: - If so, just evaluate this function at each specific value of $\theta$ that is desired. 5. Negate and form reciprocal.