Question: Let Y1 . .., Yn be a random sample from a distribution with the following probability density function: f (y; 0) = by(0-1) 0 0

Let Y1 . .., Yn be a random sample from a distribution with the following probability density function: f (y; 0) = by(0-1) 00 and f(y; 0) = 0 otherwise. (a) Write down the likelihood function for 0 from this sample. (b) Show that IIt , Y is a sufficient statistic for 0. (c) Find the maximum likelihood estimator (MLE) of 0. (d) Verify that the MLE is a function of the sufficient statistic in part (b). (e) Find the expected information for 0. (f) Write down the test statistics corresponding to each of the following tests: (i) score test; (ii) approximate Wald test

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