A simple CI

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?
unanswered

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=
unanswered

1 answer

1 - Yes
2 - 0.4