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Competitive Stats
Q33Section I (Objective (Q1–Q80))33 of 79

Statistical Inference — Fisher information via second derivative

Let x1,x2,…,xnx_1,x_2,…,x_n be a random sample from the distribution having pdf f(x,θ)=3θ3(x+θ)−4f(x,\theta)=3\theta^3(x+\theta)^{-4}; 0<x<∞0<x<\infty, θ>0\theta>0. What is E(∂2ln⁡f∂θ2)E\left(\frac{\partial^2\ln f}{\partial\theta^2}\right) equal to?

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