Question

arccoth Cz)- 1/2 ln (z+1)/(z-1)) Screenshot 2019-01-17 at 20.14.00 CSC (x) 6 Consider taking a simple random sample (SRS) of size 2 from the population and assume further that E(r2)Xwhere Xis the population mean. (0) Show that the estimato is an unbiased estimator of X XN with population variance S2. Suppose that r1 and r2 are obtained (1 mark) (5 marks,) (4 marks) (-x)tan Cx) (i) Show that cov(1,2) i) Using the result from(ii) show that var ()1- (iv) Using the central limit theorem find a 95% CI fr X assuming that ri = 4.3 I 2 h arallelogran. and r2- 3.7 and that the population is of size 100 marks うr 2. (v) Justify whether your confidence interval in part) s reliable or not (1 mark) csch (2) cos (iz) (vi) Suppose that in an SRS of size 2 only and are available instead of ri and 2. Instead of using an estimator of X an investigator proposcs an estimator of X2. They propose the following estimatorェse rit ri for some k E R+, kメ2 and 2 N. Discuss when rse is unbiased for X-and (5 marks) in (-x) sin(x) P(x) csch(x) Ce-e RCx Qx) whether this would be a sensible estimator in practice 2 a +(n-1)o 2 180

Answer 1