probability - confidence interval for conditional probabilities -

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is there possibility create confidence interval conditional probabilities? found formula create ci probabilities, not special case.

confidence intervals

i think mean confidence interval a random variable. example, if have continuous real-valued random variable x, like

p(a <= x <= b) = 0.95

meaning 95% confident x between , b.

conditional confidence intervals

a conditional confidence interval statement like

p(a <= x <= b | y = y) = 0.95

meaning, when y y, 95% confident x between , b, y other random variable.


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