Statistics - Confidence Intervals - \(\displaystyle{P}{\left({X}{>}{1}\right)}\) \(\displaystyle{X}_{{1}},\cdots{c},{X}_{{n}}\sim{U}{\left({0},{2}{p}\right)}\)

sexoagotadorogyr

sexoagotadorogyr

Answered question

2022-03-31

Statistics - Confidence Intervals -
P(X>1)
X1,c,XnU(0,2p)

Answer & Explanation

Wilson Rivas

Wilson Rivas

Beginner2022-04-01Added 12 answers

Step 1
Details of Comment: From what you say, I assume you have lower and upper bounds for a 2-sided 95% CI for p. Say that these bounds are L and U. Then
P(L<p<U)=0.95.
Manipulate the inequality L<p<U to get 2L<2p<2U, then 12L<12p<12U and finally
P(112L<112p=τ<112U)=0.95,
which would give the 95% CI (112L, 12U) for
τ=P(X>1)=112p.
All of this depends on what you have told me. I have not checked the correctness of that. I'm just filling in details of my comment as you requested.
This is not fundamentally different (or more difficult) than manipulating the probability statement
P(1.96<Z=Xμσn<1.96)=0.95
to get the CI X±1.96σn for μ when sampling from normal data with σ known.

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