Suppose that X is a discrete random variable with
P(X = 0) = 2/3µ
P(X= 1) = 1/3µ
P(X= 2) = 2/3(1 - µ)
P(X= 3) = 1/3(1 - µ)
where 0 <= μ <= 1 is a parameter. Thefollowing 10 independent observations were taken from such adistribution: (3,0,2,1,3,2,1,0,2,1).
(a) Find the method of moments estimate of μ
(b) Find an approximate standart error for your estimate.
(c) What is the maximum likelihood estimate of μ?
(d) What is an approximate standard error of the maximum likelihood estimate?