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[answered] Let S follow Binomial(N, ) where is known but N is unknown.


Let?S?follow Binomial(N, ?) where???is?known?but?N?is?unknown.?

(a) Show that the M.L.E of?N, say ?N (N hat), is the largest integer not exceeding?S/????1.

(b)??Show that as?N?? ?,??N/N??p?1.

(c)??If?S?follows Binomial(N, ?) what is the most likely value (out of 0,?1,?2, . . . , N) to be?assumed by?S? Suppose?S?indeed assumes this value.?What is the estimator of?N?based on?this value?

 


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