Let f(x, y 1, 2, 3, 4) be the bivariate pdf for the uniform distribution on the rectangle with lower left corner (1, 2) and upper right corner (3, 4) in 2 The parameters satisfy 1 2 and 3 4 Let (X1, Y1), , (Xn, Yn) be a random sample from this pdf Find a four dimensional sufficient statistic for (1, 2, 3, 4)

Question: Let f(x, y|1, 2, 3, 4) be the bivariate pdf for the uniform distribution on the rectangle with lower left corner (1, 2) and upper

Let f(x, y|θ1, θ2, θ3, θ4) be the bivariate pdf for the uniform on the rectangle with lower left corner (θ1, θ2) and upper right corner (θ3, θ4) in ℜ2. The parameters satisfy θ1 < θ2 and θ3 < θ4. Let (X1, Y1),..., (Xn, Yn) be a random sample from this pdf. Find a four-dimensional sufficient statistic for (θ1, θ2, θ3, θ4).

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