1. Let q; > 0 be a population parameter, and let X l , X 2, , X n be a random sample from a distribution with probability density function 2 105311) : 2 9K A, , x> 0. zero otherwise. m Recall: W = X2 has Gamma( (1 = % 9 = w) distribution. X2: X2 h) Recall that the maximum likelihood estimator of \\|J is l]!- \" 2X Xi . 2H 3: 1' Is {[1 a consistent estimator of It}? Justii your answer. (NOT enough to say \"because it is the maximum likelihood estimator\") \"Hint\": Start with the WLLN and W OR use part (f). .. 2 i) Recall that a method of moments estimator of w is 1|! = 11: ( X ) . ls \\IJ a consistent estimator of u)? Justify your answer. (NOT enough to say \"because it is a method of moments estimator\") \"Hint": Start with the WLLN and X. n j) Constructa consistent estimator of w based on 2 X (-4. i=1 \"Hint\": x4 = W2