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 Nj 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, NV3) and Analyst B knows only (N1, N2 + N3). Qu. Show that (N1, N2, N3) follows a multinomial distribution with probabilities 1 - 0, 0(1 - 0) and 02, respectively (s marks). Note that a random variable (X, Y, Z) follows a multinomial distribution with size n and proba- bilities p, q, andr = 1 - p - qif X + Y + Z = n and their joint p.m.f. is n! P(X = a, Y = b, Z = c) = a!b!c! P qrc for all non-negative integers a, b, c such that a + b + c = n