Q27Section I (Objective (Q1–Q80))27 of 80

Statistical Inference — Fisher information carried by a linear combination of iid normals

Let $X_1, X_2$ and $X_3$ be iid normal variates with mean $\theta$ and variance 1. Define a statistic $T=X_1-X_2-X_3$ for unknown parameter $\theta$ . Then the Fisher information contained in statistic T is

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