ssume X is a discrete random variable that takes values in {1, 2, 3}, with probability defined by Pr(X = 1) = 1 Pr(X = 2) = 21 Pr(X = 3) = 2, where = [1, 2] is an unknown parameter to be estimated. Now assume we observe a sequence D := {x(1), x(2), . . . , x(n)} that is independent and identi- cally distributed (i.i.d.) from the distribution. We assume the number of observations of the values: 1, 2, 3 in D are s1, s2, s3, respectively. (a) [5 points] To ensure that Pr(X = i) is a valid probability mass function, what constraint should we put on = [1, 2]? Write your answers quantitatively as expressions that include 1 and 2. (b) [5 points] Write down the joint probability of the data sequence Pr (D | ) = Pr n x(1), . . . , x(n)o | , and the log probability log Pr(D | ). (c) [5 points] Calculate the maximum likelihood estimation of based on the sequence D