Let X1, ...,Xn be a random sample from a folded normal distribution with density f(x; ) = 2/ exp{2x2/2}, for x > 0,> 0. (i)

Let X1, ...,Xn be a random sample from a folded normal distribution with density f(x; θ) = 2/πθ exp{−θ2x2/2}, for x > 0,θ> 0. (i) Derive the UMP test for H0 : θ = θ0 against H1 : θ>θ0. (ii) Show that the power function is increasing.