In: Statistics and Probability
a. Suppose that X is a discrete random variable with pmf f(x) = (2 + θ(2 − x))/ 6 , x = 1, 2, 3, where the parameter θ belongs to the parameter space Ω = (θ : −2 < θ < 2). Suppose further that a random sample X1, X2, X3, X4 is taken from this distribution, and the four observed values are {x1, x2, x3, x4} = {3, 2, 3, 1}. Find the maximum likelihood estimate of θ. b. Repeat part a) but assume that Ω = {−1, 0, 1}