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Let theta be an unknown parameter, and let X be uniform on the interval [theta - 0.5, theta +0.5]. I form a confidence interval of

Let theta be an unknown parameter, and let X be uniform on the interval [theta - 0.5, theta +0.5]. I form a confidence interval of the form [X-a,X+a]. What is the narrowest confidence interval of this type (i.e., what is the smallest possible choice of a) if I want to have an 80% confidence interval

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