Question 4 Consider an unknown parameter 9. It can be estimated with either 6] with variance 146]) = of or, HA2 with variance V(2) = a3. The estimators are correlated with Coowl, 9}) = 012 , and, both 6] and 91; are unbiased estimator for 6. Consider the unbiased estimator 63 = a - 9'; + (1 - a) - 0;, where a 6 1R. What value of a minimizes the variance of 63? Solution to Question 4 Your answers go here. Question 5 Consider a sample of three observations X1, X2, - - - ,Xn from a normal distribution with mean a and variance 1, where ,u is unknown. That is X1, X 2, - -- ,X" ~ N(,u, 1). Consider two distinct estimators for n: 1=x1+xg + ig {I2 = 110131 + 110352 + nis- For what values of ,u does g achieve a lower MSE than it] (if any)? Solution to Question 5 Your answers go here