Continuing the last problem, prove that Jii has a maximum at r = 1 2 when i

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Continuing the last problem, prove that Jθiθi has a maximum at r = 1 2

when θi is fixed. Use this fact to show that Jθiθi ≤ 1/[2θi(1 − θi)].

Given a known retention probability r, this inequality proves that the asymptotic standard error of the estimated θi will be at least √2 times greater than that calculated for a simple binomial experiment with success probability θ.

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Applied Probability

ISBN: 9780387004259

1st Edition

Authors: Kenneth Lange

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Question Posted: Oct 31, 2024 03:00 AM

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Continuing the last problem, prove that Jii has a maximum at r = 1 2 when i

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Applied Probability

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