Let X1, , Xn be i i d with a Bernoulli distribution that has parameter p Let Y We wish to find a coefficient confidence interval for p of the form (q(y), 1) Prove that, if Y y is observed, then q(y) should be chosen to be the smallest value p0 such that Pr(Y y p p0) 1

Question: Let X1, . . . , Xn be i.i.d. with a Bernoulli distribution that has parameter p. Let Y = We wish to find a

Let X1, . . . , Xn be i.i.d. with a Bernoulli that has parameter p. Let Y = We wish to find a coefficient γ confidence interval for p of the form (q(y), 1). Prove that, if Y = y is observed, then q(y) should be chosen to be the smallest value p0 such that
Pr(Y ≥ y|p = p0) ≥ 1− γ .

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