Let x be a random variable with a distribution p in p t f

Question

Let X be a random variable with a distribution P_θ in {P_θ: θ ∈ Θ}, f_θ be the p.d.f. of P_θ w.r.t. a measure ν, A be an event, and PA = {f_θI_A/P_θ(A) : θ ∈ Θ}.

(a) Show that if T (X) is sufficient for P_θ ∈ P, then it is sufficient for P_θ ∈ P_A.

(b) Show that if T is sufficient and complete for P_θ ∈ P, then it is complete for P_θ ∈ P_A.