2. [25 points] Let X,..., Xn be i.i.d. random variables from N(0, 0) with pdf 1...

Transcribed Image Text:

2. [25 points] Let X₁,..., Xn be i.i.d. random variables from N(0, 0) with pdf 1 √2π0 (a) Consider an estimator of 0 defined as f(x; 0) = = 1 where 0 0 <∞. 72 Σx². i=1 Compute the mean and the variance of s². Remark. • You may use the fact that Var[X²] = 20² where X~ N (0,0). (b) Compare the variance of s² with the Cramér-Rao lower bound. 2. [25 points] Let X₁,..., Xn be i.i.d. random variables from N(0, 0) with pdf 1 √2π0 (a) Consider an estimator of 0 defined as f(x; 0) = = 1 where 0 0 <∞. 72 Σx². i=1 Compute the mean and the variance of s². Remark. • You may use the fact that Var[X²] = 20² where X~ N (0,0). (b) Compare the variance of s² with the Cramér-Rao lower bound.