Problem 1. Suppose that X1, ..., Xn are i.i.d. following pdf given by f(x; 0) = ge , where both x and 0 are in (0, co), and A is the unknown parameter. Find a sufficient statistic for 0, which must be a real-valued continuous function of (X1, . . ., Xn). Problem 2. . Find the maximum likelihood estimator (MLE) in the example of Problem 1. . Calculate the mean of the MLE. Is the MLE unbiased? . Calculate the variance of the MLE. Does the MLE achieve the minimum variance among all unbiased estimators (for some finite sample size)? Why? Problem 3. In Problem 1, find a large sample (asymptotic) confidence interval for 0, with significance 0.01. The length of the confidence interval must be order