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Q53Section B (Part B)53 of 120

Confidence intervals — a pivot from a triangular density

Let XX be a single sample from an absolutely continuous distribution with probability density function

f(x∣θ)={2θ2(θ−x),0<x<θ0,otherwise,f(x\mid\theta)=\begin{cases}\dfrac{2}{\theta^2}(\theta-x), & 0<x<\theta\\ 0,&\text{otherwise,}\end{cases}

where θ>0\theta>0 is unknown. Which of the following intervals is a 95% confidence interval for θ\theta?

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