Suppose that X is a discrete random variable with Pr(X = 0) = 2/3µ; Pr(X = 1) =1

Question

Suppose that X is a discrete random variable with
Pr(X = 0) = 2/3µ;
Pr(X = 1) =1/3µ;
Pr(X = 2) =2/3(1 - µ);
Pr(X = 3) =1/3(1 - µ)
where 0 <= µ <= 1 is a parameter. The following 10independent observations
were taken from such a distribution:(3,0,2,1,3,2,1,0,2,1).
(b) Find an approximate standard error for your estimate.
for the part: approximate S.E. of the estimate, I have seen asolution but think that there is a mistake there. I have posted mycomments, for details please look here:

/answers-mar-10/statistics-and-probability/urgent-lifesaver-please-help-suppose-that-x-is-a-discrete-random-variable-with-prx-0_788694.aspx

(d) What is an approximate standard error of the maximum likelihoodestimate?
Here I have    Var(head) = -1/E(l''(0)   where n0=2, n1=3,n2=3,n3=2
where E(l''(0) = E [(n2+n3)/(1-)2] - E[(n0+n1)/ 2 ]
Then we can put =1/2 which we got from MLEestimate.
Is that right?

(e) if the prior distribution is uniform on [0,1], what is theposterior density?

Suppose that X is a discrete random variable with
Pr(X = 0) = 2/3µ;
Pr(X = 1) =1/3µ;
Pr(X = 2) =2/3(1 - µ);
Pr(X = 3) =1/3(1 - µ)
where 0 <= µ <= 1 is a parameter. The following 10independent observations
were taken from such a distribution:(3,0,2,1,3,2,1,0,2,1).
(b) Find an approximate standard error for your estimate.
for the part: approximate S.E. of the estimate, I have seen asolution but think that there is a mistake there. I have posted mycomments, for details please look here:

/answers-mar-10/statistics-and-probability/urgent-lifesaver-please-help-suppose-that-x-is-a-discrete-random-variable-with-prx-0_788694.aspx

(d) What is an approximate standard error of the maximum likelihoodestimate?

Explanation / Answer

I would appreciate if any of these subpoints would be either corrected, confirmed, or answered.

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