Let X be a discrete random variable with state space {1,2,3}, a hypothetical three sided die. Suppose that the probabilities associated with the state space are P(X = 1) = 40, == P(X = 2) = 30, P(X=3)= 1 70. Q1 Calculate the range of possible values of the parameter 0. Q2 Calculate the Maximum Likelihood Estimator of X. (This estimator should be expressed in terms of x1, x2, and x3, where xi is the number of times i shows up in the data sample set. If 1 shows us five times, then x1 = 5.) (*) Let X1, XN be a sample set of Uniform (a, b), where b> a and a and b are unknown parameters. Find the MLE and b. (Write out the likelihood function in terms of indicator functions. An indicator function 1s(x) gives output 1 when x is in the set S and outputs 0 when x is not in the set S.)