(Continuation of Exercise 6.4-2.) In sampling from a

QUESTION:

(Continuation of Exercise 6.4-2.) In sampling from a normal distribution with known mean \(\mu\), the maximum likelihood estimator of \(\theta=\sigma^{2}\) is \(\hat{\theta}=\sum_{i=1}^{n}\left(X_{i}-\mu\right)^{2} / n\)

(a) Determine the Rao-Cramér lower bound.

(b) What is the approximate distribution of \(\hat{\theta}\)?

(c) What is the exact distribution of \(n \hat{\theta} / \theta\), where \(\theta=\sigma^{2}\) ?

Equation Transcription:

Text Transcription:

 mu

theta=sigma^2

Hat thea =sum_i=1^n( X_i-mu)^2/n

Hat theta

 n hat theta/theta