Question: (Likelihood Identities) Suppose that U is a continuous random variable with the p.d.f. f (u: ), which is twice continuously differentiable in . Let (U,

(Likelihood Identities) Suppose that U is a continuous random variable with the p.d.f. f (u: θ₀), which is twice continuously differentiable in θ₀. Let (U₁, ..., Uₙ) be a random sample of U.

(a) Prove that E[Lθ₀(θ₀)] = 0.

(h) Suppose also that Var[Lθ(θ₀)] exists. Prove that E[Lθθ(θ₀)] = −Var[Lθ(θ₀)].

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