Where 0 lt mu lt 1 is a parameter. thefollowing 10, Ask an Expert

Statistics

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 likelihoodestimate?

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