Correct answer: (D) −2ln(1/2+X/π) is central χ² with one degree of freedom.
Explanation
Tan of a uniform angle is standard Cauchy;its reciprocal cot has the same law. The transformed U=1/2+X/π is Uniform(0,1),so −ln U∼Exp(1). Consequently −2ln U is χ²₂,not χ²₁. **D**.
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