Find sufficient statistics (or show that they do not exist) for parameter in the following distributions: (i) f(x,)=(x/2)ex2/22 for x > 0 (Rayleigh). (ii)

Find sufficient statistics (or show that they do not exist) for parameter θ in the following distributions: (i) f(x,θ)=(x/θ2)e−x2/2θ2 for x > 0 (Rayleigh). (ii) f(x,θ) =

(1/2θ)e−|x|θ (double exponential). (iii) BETA(θ, 2θ). (iv) U[θ, 2θ]. (v) GAM(θ,θ).

(vi) f(x,θ) = {π[1 + (x − θ)2]}−1 (Cauchy).