Let {Xj} i.i.d. N(, ). Show that Pn j=1 Xj , Pn j=1 X2 j

Let {Xj} ∼ i.i.d. N(μ, σ). Show that

³Pn j=1 Xj , Pn j=1 X2 j

´

is a sufficient and complete statistic for θ = (μ, σ).