題組內容

三、 A random sample \( X_1, X_2, \dots, X_n \) of size \( n \) is taken from \( N(\mu, \sigma^2) \), where the variance \( \theta = \sigma^2 \) is such that \( 0 < \theta < \infty \) and \( \mu \) is a known real number.

2. Show that this estimator \( \hat{\theta} \) is an unbiased estimator of \( \theta \)? (10分)