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Refer to the previous problem and suppose that both m and s 2 are unknown. Then a con?dence interval for m with approximate con?dence coef- ?cient 1 - a is given be relation (20).

i) What does this interval become for n = 100 and a = 0.05?

ii) Show that the length of this con?dence interval tends to 0 in probability (and also a.s.) as n ® ¥;

iii) Discuss part (i) for the case that the underlying distribution is B(1, q), q Î Ù = (0, 1) or P(q), q Î Ù = (0, ¥).

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