Continuing the last problem, prove that Jii has a maximum at r = 1 2 when i is fixed. Use this fact to show that

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.