Let X₁,X₂, . . . , X_n be a random sample from a N(θ, σ²) distribution, where σ² is fixed but −∞ < θ < ∞.
(a) Show that the mle of θ is ‾X.
(b) If θ is restricted by 0 ≤ θ < ∞, show that the mle of θ is ^{^}θ = max{0,‾X}.