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Exercise: A simple CI

1/2 points (graded)
Let θ be an unknown parameter, and let X be uniform on the interval [θ−0.5,θ+0.5] .

Is [X−2,X+2] an 80% confidence interval?

YES correct

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?

a= ????

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