yt=a+ut,t=1,,T where ut is an error term. The error terms ut 's are iid and normally distributed with mean zero and variance 2 : utiidN(0,2). 1. Derive the Maximum Likelihood estimator of a 2. Derive the Maximum Likelihood estimator of 2 3. Derive the asymptotic distribution of a^ 4. Is the distribution of a^ the same as if we had estimated the parameter by linear regression? What does Cramer-Rao tell us about the linear regression estimate of a ? 5. Derive an expression for the likelihood ratio test for the hypothesis a=2. What is the distribution of this test? For which values of the test statistics is the hypothesis rejected if the test is done at a 95% confidence level? yt=a+ut,t=1,,T where ut is an error term. The error terms ut 's are iid and normally distributed with mean zero and variance 2 : utiidN(0,2). 1. Derive the Maximum Likelihood estimator of a 2. Derive the Maximum Likelihood estimator of 2 3. Derive the asymptotic distribution of a^ 4. Is the distribution of a^ the same as if we had estimated the parameter by linear regression? What does Cramer-Rao tell us about the linear regression estimate of a ? 5. Derive an expression for the likelihood ratio test for the hypothesis a=2. What is the distribution of this test? For which values of the test statistics is the hypothesis rejected if the test is done at a 95% confidence level