A. Suppose that X takes values 1, 10 and 100 with probabilities depending on 0. That is X P[X=x|01] P[X=x|02] P[X=x|03] 1 0.3 0.2 0.5 10 0.3 0.5 0.25 100 0.4 0.3 0.25 i. ii. Based on one observation, X, from this distribution what is the maximum likelihood estimator of 0? Now suppose we have two independent observations, (X1, X2), from this distribution. Let S be the sum of these two observations a) Find the distribution of S given 0=0k, k=1,..., 3. b) Suppose that (X1, X2) were not recorded but that S was. What is the mle of 0? c) Is S a sufficient statistic? Prove or disprove. d) How would the MLE you found in b change if you observed (X1, X2)