Chapter 3 Warm-up

Recall: We learned about Fisher Information \((I)\) defined when \(\theta\) is unidimensional by the second derivative of the log likelihood. (Jordan M.)

\[I(\theta) = -E\left[ \frac{\partial^2}{\partial \theta^2} log f(X;\theta)| \theta\right]\]

1. Find the Fisher Information for a Bernoulli Distribution \(f(X|\theta)=p^x(1-p)^{1-x}\).

 

2. What’s important about Fisher Information?