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3. [18 marks] Let Y1 . .., Y, denote a random sample from the probability density func- tion f(y: 0) = (0+1)y 0-1 and f(y; 0) = 0 otherwise. (a) Write down the likelihood function and the log-likelihood function for 0. (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) Provide an approximate 95% confidence interval for 0 in large samples, written in terms of the maximum likelihood estimate d. (g) Write down the test statistics corresponding to each of the following tests: i. likelihood ratio test ii. score test; iii. Wald test iv. approximate Wald test