Consider the population described by the probability distribution shown in the table. The random variable x is observed twice. If these observations are independent, all the different samples of size 2 and their probabilities are shown in the accompanying table. Complete parts a through c below. Click the icon to view the table. More info - X a. Show that x is an unbiased estimator of p. Find p and E ( H = 2.8 X 1 2 3 4 5 E(x) = 2.8 p(x) 0.1 0.4 0.2 0.2 0.1 (Type integers or decimals.) X 1.0 1.5 2.0 2.5 3 3.5 4 4.5 5 Is x an unbiased estimator of u? P(x) 0.01 0.08 0.2 0.2 0.22 0.16 0.08 0.04 0.01 O A. No, since E (x) = H. Full data set O B. No, since E (x) # H. Sample Mean Probability Sample Mean Probability O C. Yes, since E (x) # H. 1,1 1.0 0.01 3,4 3.5 0.04 1,2 1.5 0.04 3,5 4.0 0.02 D. Yes, since E (x) = H. 1,3 2.0 0.02 4.1 2.5 0.02 1,4 2.5 0.02 4.2 3.0 0.08 b. Find of. 1,5 3.0 0.01 4.3 3.5 0.04 2,1 1.5 0.04 4.4 4.0 0.04 G= = (Round to three decimal places as needed.) 2,2 2.0 0.16 4.5 4.5 0.02 2.3 2.5 0.08 5,1 3.0 0.01 2,4 3.0 0.08 5.2 3.5 0.04 2.5 3.5 0.04 5.3 4.0 0.02 3.1 2.0 0.02 5.4 4.5 0.02 3,2 2.5 0.08 5,5 5.0 0.01 3.3 3.0 0.04