Question: Let (X1, X2, ..., Xn) denote a random sample from the density function f(x|0) = -0 In(0) I(x > 0), where 0 E (0, 1)

Let (X1, X2, ..., Xn) denote a random sample from the density function f(x|0) = -0" In(0) I(x > 0), where 0 E (0, 1) is an unknown parameter. Denote N, to be the number of observations among the sample elements which belong to the interval (j-1, j], j = 1, 2 and N3 = n-N1-N2. For confidentiality, only summaries of the sample are released to two analysts, such that Analyst A knows only (N1, N2, N3) and Analyst B knows only ( N1, N2 + N3).Q3. Based on the data released to Analyst A, (a) Show that the likelihood function of 0 is given by (1 - 0) NitN2gN2+2N3 (3 marks). (b) Find the Fisher information about 0 (4 marks). (c) Find the MLE of @ and state its large-sample distribution

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