Suppose that X is a discrete random variable with: P(X=0) = (2/3)theta P(X=1) = (1/3)theta P(X=2) = (2/3)(1-theta) P(X=3) = (1/3)(1-theta) where theta: [0,1] is a parameter. The following 10 independent observations were taken from such a distribution: (3,0,2,1,3,2,1,0,2,1)
a. Find the moment of methods estimate of theta
b. Find an approximate standard error for your estimate
c. What is the maximum likelihood estimate of theta?
d. What is an approximate standard error of the maximum likelihood estimate?