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).Q2. Based on the complete sample (X1, X2, . . . , X\"), {a} Write down an expression for the likelihood function of H {1 marks}. {b} Derive a scalar suieient statistics For 3 (1 marks). (c) Find the Fisher Information about 3 {4 marks). Note that X follows some exponential distri- bution