L x be a single observation from n- 1 1 if

Question

Let X be a single observation from N(θ^{- 1}, 1) if θ < 0,="" n(0,="" 1)="" if="" θ="0," and="" n(θ="" +="" 1,="" 1)="" if="" θ=""> 0.

(a) Show that the distribution of X is in a family with monotone likelihood ratio.

(b) Construct a Θ′ -UMA lower confidence bound for θ with confidence coefficient 1 - α, where Θ′ = (-∞, θ).