Let X1,…,Xn∼i. i.d. N(0,σ2) , for some σ2>0 . Let σ2ˆ=1n∑i=1nX2i, andσ2˜=1n∑i=1n(Xi−X¯¯¯¯n)2. Argue that both proposed estimators σ2ˆ and σ2˜ below are consistent and asymptotically normal. Then, give their asymptotic variances V(σ2ˆ) and V(σ2˜) and decide if one of them is always bigger than the other. Hint: Use the multivariate Delta method. Also see Recitation 5 Inference for the Variance of a Gaussian distribution. V(σ2ˆ)=