Question: Subject: Statistical Interference-1) Q1 : Let X1, X2... Xn be the random sample from the density: (, ) = (1 + ) (1+) , 0

Subject: Statistical Interference-1)

Q1: Let X1, X2... Xn be the random sample from the density:

(, ) = (1 + ) (1+) , 0 < <

(a) Find an unbiased estimator of .(2.5 Marks)

(b) Find a consistent estimator of .(2.5 Marks)

(c) Find a sufficient statistic of .(2.5 Marks)

(d)Find a complete statistic of . (2.5 Marks)

(e) Find UMVUE of1 . Find its variance and compare with Cramer-Rao lower bound.(05 Marks)

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