Reference no: EM131851972

Let X be a single sample from P_θ. Find the Fisher information I(θ) in the following cases.

(a) P_θ is the N(µ, σ²) distribution with θ = µ ∈ R.

(b) P_θ is the N(µ, σ²) distribution with θ = σ² > 0.

(c) P_θ is the N(µ, σ²) distribution with θ = σ > 0.

(d) P_θ is the N(σ, σ²) distribution with θ = σ > 0.

(e) P_θ is the N(µ, σ²) distribution with θ = (µ, σ²) ∈ R × (0, ∞).

(f) P_θ is the negative binomial distribution NB(θ, r) with θ ∈ (0, 1).

(g) P_θ is the gamma distribution Γ(α, γ) with θ = (α, γ) ∈ (0, ∞) × (0, ∞).

(h) P_θ is the beta distribution B(α, β) with θ = (α, β) ∈ (0, 1)×(0, 1).