Question (3): Point Estimation of Parameters and Sampling Distributions [35 points] 1) Suppose that 8, and are estimators of the parameter 8. We know that E(8) = 0, E(8) = 8/3, V(8) = 10, V(8) = 4. For which value of the parameter 8 is better than 8? In what sense is it better? II) Let X be a geometric random variable with parameter 0 < p < 1, where f(x)= (1-p)* p, x = 1,2,.... The mean and variance of X are 1/p and (1-P)/p, respectively. Based on a random sample of size n, find an estimator of p by: a) the method of moments, and b) the method of maximum likelihood estimation. III) Suppose that X-N(u, 40), and let the prior density for u be N(4,8). For a random sample of size 25, the value * = 4.85 is obtained. What are the maximum-likelihood and Bayes estimates of ?